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Enlargement - class-X

Description: enlargement
Number of Questions: 19
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Tags: maths exploring geometrical figures similarity enlargement and scale drawing mapping your way
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A rectangle of length $4\ cm$ and breadth $3\ cm$ is scaled up $2$ times. What is the new length of the rectangle?

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. $6\ cm$

  2. $4\ cm$

  3. $8\ cm$

  4. $3\ cm$

Show answer
Correct Option: C
Explanation:

The size of the rectangle become double when it is scaled up $2$ times.

So new length $=2\times 4=8\ \ cm$
So option $C$ is correct.

A circle of radius $7\ cm$ is scaled $3$ times. Then the perimeter of the circle become:

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. $3$ times the original perimeter

  2. $6$ times the original perimeter

  3. $9$ times the original perimeter

  4. Doesn't change

Show answer
Correct Option: A
Explanation:

Radius of circle $=7 \ \ cm$

Perimeter $=2\pi r=2\times \pi\times7=14\pi\ \ cm$
When scaled $3$ times
New radius $=3\times 7=21 \ \ cm$
New Perimeter $=2\pi r=2\times \pi\times21=42\pi\ \ cm$
Ratio of perimeters $=\dfrac{42\pi}{14\pi}=3$
So the perimeter becomes three times.

If one shape becomes another using a resize, then the shapes are __________. 

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. similar

  2. congruent

  3. mirror images

  4. none of the above

Show answer
Correct Option: A
Explanation:

Resizing leads to change in scale factor and if the scale factor remains equal, then the figures will be similar to each other.

If one shape becomes another using rotation / reflection, then the shapes are __________.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. similar

  2. congruent

  3. mirror images

  4. none of the above

Show answer
Correct Option: B
Explanation:

If the size of the figure does not get affected by rotation or reflection, then the figure will remain same and it will be congruent.

If the area of square is $36\pi \ \text{cm}^2$. If its length is scaled three times, what would be its new area?

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. $342\pi$

  2. $324\pi$

  3. $352\pi$

  4. $322\pi$

Show answer
Correct Option: B
Explanation:

Area of square whose side is $a =a^2$ 

If its length is scaled three times, then area $=9a^2$
Therefore, new area $=9\times 36\pi \text{cm}^2=324\pi \text{cm}^2$

The measure of $3.4\ cm$ on a $2:1$ scaled model will be:

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. $3.4\ cm$

  2. $6.8\ cm$

  3. $1.7\ cm$

  4. $4.5\ cm$

Show answer
Correct Option: C
Explanation:

Let orignal length $=l$ and scales length $=sl$

$\dfrac { l }{ sl } =\dfrac { 2 }{ 1 } \ \dfrac { 3.4 }{ sl } =\dfrac { 2 }{ 1 } \ \Rightarrow sl=1.7$
So option $C$ is correct.

A $30-60-90$ degree triangle is scaled $1.5$ times. The new angles of the triangle are:

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. $45-45-90$

  2. $30-60-90$

  3. $37-53-90$

  4. $60-60-60$

Show answer
Correct Option: B
Explanation:

When the triangle is scaled $1.5$ times then length of each side become $1.5$ times but the angle remains the same.

So the new angles are $30-60-90$
Option $B$ is correct.

A submarine is scaled down to $\dfrac{1}{100}$ times for making a model. If the length of the submarine in the scaled down model was $100\ cm$, what is the original length of the submarine?

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. $100\ cm$

  2. $500\ m$

  3. $100\ m$

  4. $500\ cm$

Show answer
Correct Option: C
Explanation:
$L = OriginalLength$
$l=ScaledDownLength= 100cm = 1m$

$\cfrac{l}{L}= \cfrac{1}{100}$
$\cfrac{1m}{L} = \cfrac{1}{100}$
$L= 100m$


A triangle ABC has been enlarged by scale factor m= 2.5 to the triangle A' B' C'. Calculate the length of C' A' if CA=4 cm.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. 10

  2. 8

  3. 6

  4. 12

Show answer
Correct Option: A
Explanation:

$\triangle ABC$ is enlarged to $\triangle A'B'C'$,
Thus, $\dfrac{C'A'}{CA} = 2.5$
Therefore, $\dfrac{C'A'}{4} = 2.5$
$\Rightarrow C'A' = 4 \times 2.5$
$\Rightarrow C'A' = 10$ cm 

A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find OA, if OA'= 6 cm.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. 2 cm

  2. 3 cm

  3. 4 cm

  4. none of the above 

Show answer
Correct Option: A
Explanation:

$\triangle ABC$ is enlarged to $\triangle A'B'C'$,
Thus, $\dfrac{OA'}{OA} = 3$
$\Rightarrow \dfrac{6}{OA} = 3$
$\Rightarrow OA = \dfrac{6}{3}$
$\Rightarrow OA = 2 $ cm

A triangle LMN has been reduced by scale factor 0.8 to the triangle L' M' N'. Calculate the length of LM, if L' M'= 5.4 cm.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. 6.75 cm

  2. 5.75 cm

  3. 6.25 cm

  4. none of the above

Show answer
Correct Option: A
Explanation:

$\triangle LMN$ is reduced to $\triangle L'M'N'$,
Thus, $\dfrac{L'M'}{LM} = 0.8$
$\Rightarrow \dfrac{5.4}{LM} = 0.8$
$\Rightarrow LM = \dfrac{5.4}{0.8}$
$\Rightarrow LM = 6.75$ cm 

A triangle LMN has been reduced by scale factor 0.8 to the triangle L' M' N'. Calculate the length of M' N'. if MN= 8 cm.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. 6.4 cm

  2. 4.4 cm

  3. 5.4 cm

  4. none of the above

Show answer
Correct Option: A
Explanation:

$\triangle LMN$ is reduced to $\triangle L'M'N'$,
Thus, $\dfrac{M'N'}{MN} = 0.8$
$\Rightarrow \dfrac{M'N'}{8} = 0.8$
$\Rightarrow M'N' = 0.8 \times 8$
$\Rightarrow M'N' = 6.4 $ cm 

A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find BC. if B'C'= 15 cm.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. 6 cm

  2. 5 cm

  3. 7 cm

  4. none of the above

Show answer
Correct Option: B
Explanation:

$\triangle ABC$ is enlarged to $\triangle A'B'C'$,
Thus, $\dfrac{B'C'}{BC} = 3$
$\Rightarrow \dfrac{B'C'}{BC} = 3$
$\Rightarrow BC = \dfrac{15}{3}$
$\Rightarrow BC = 5$ cm 

A has a pair of triangles with corresponding sides proportional, and B has a pair of pentagons with corresponding sides proportional.
$S _1 \equiv $ A's triangles must be similar
$S _2 \equiv $ B's pentagons must be similar 
Which of the following statement is correct ? 

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. $S _1$ is true, but $S _2$ is not true.

  2. $S _2$ is true, but $S _1$ is not true.

  3. Both $S _1$ and $S _2$ are true

  4. Neither $S _1$ and $S _2$ are true

Show answer
Correct Option: A
Explanation:

For similarity of triangles we have SSS criteria. So $S _1$ is true. 
But for polygons to be similar, the corresponding sides must be in equal ratio as well as the corresponding angles must be congruent.

Since, there is nothing mentioned about the angles of the pentagons, so $S _2$ is false.

A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find A'B', if AB = 4cm.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. 12 cm

  2. 14 cm

  3. 22 cm

  4. none of the above

Show answer
Correct Option: A
Explanation:

$\triangle ABC$ is enlarged to $\triangle A'B'C'$,
Thus, $\dfrac{A'B'}{AB} = 3$
$\Rightarrow \dfrac{A'B'}{4} = 3$
$\rightarrow A'B' = 4 \times 3$
$\Rightarrow A'B' = 12 $ cm 

A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find OC', if  OC=21 cm.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. 63 cm

  2. 53 cm

  3. 43 cm

  4. none of the above

Show answer
Correct Option: A
Explanation:

$\triangle ABC$ is enlarged to $\triangle A'B'C'$,
Thus, $\dfrac{OC'}{OC} = 3$
$\Rightarrow \dfrac{OC'}{21} = 3$
$\Rightarrow OC' = 21 \times 3$
$\Rightarrow OC' = 63 $ cm

A flagstaff $17.5$ m high casts a shaded length of $40.25$ m. The height of the building which costs a shadow of length $28.75$ m under similar conditions will be:

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. $10$ m

  2. $12.5$ m

  3. $17.5$ m

  4. $21.25$ m

Show answer
Correct Option: B
Explanation:

Flagstaff and shade forms right triangle with height $17.5$ m and base $40.25$ m

$\dfrac{17.5}{40.25} = \tan(\theta)$
under similar conditions $\theta$ will remain same.
Lets assume height of the building as $H$
Hence, $ \tan(\theta)=\dfrac{17.5}{40.25}$ $ = \dfrac {H}{20.75}$
$\Rightarrow  H= 12.5$ m

The ratio of the lengths of the corresponding sides of $2$ similar right angled triangles is $2:5$. If the length of the hypotenuse of the smaller triangle is $5$ inches, find the length of the hypotenuse of the larger triangle (in inches):

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. 2

  2. 2.5

  3. 7

  4. 10

  5. 12.5

Show answer
Correct Option: E
Explanation:

Ratio of the length of the sides of the two triangle $=2:5$

If hypotenuse  of small triangle $=5$ inches
Let the hypotenuse of  larger triangle $=x$
$\therefore \dfrac{5}{x}=\dfrac{2}{5}$
$\therefore  x=\dfrac{25}{2}=12.5$  inches

If the image of an object is enlarged, then what would be the effect on scale factor, $k?$

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. $k$ will remain same for both.

  2. $k>1$ for enlarged image.

  3. $k<1$ for enlarged image.

  4. none of the above

Show answer
Correct Option: B
Explanation:


If image is enlarged, $k>1.$
If image size does not change, then $k=1.$
If image size is reduced, $k<1.$

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