Tag: diagonal of cube and cuboid

Questions Related to diagonal of cube and cuboid

Is $(3,\,4,\,6)$ a pythagorean triplet?
maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. Yes

  2. No

  3. Cannot be deermined

  4. None

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Correct Option: B
Explanation:

$ {3}^{2} + {4}^{2} = 9 + 16 = 25 $
$ {6}^{2} = 36 $

Since, $  {3}^{2} + {4}^{2} \neq {6}^{2} , (3,4,6) $ is not a pythagorean triplet.

To get _________ triplets we use the general form $ 2m, m^2+1, m^2-1$.

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. Square number

  2. Consecutive number

  3. Repeated

  4. Pythagorean

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Correct Option: D
Explanation:

$ 2m, m^2+1, m^2-1$ forms are used to get Pythagorean Triplets.

Are all of the following triplets are pythagorean?
$(8,\,15,\,17)$
$(16,\,63,\,65)$
$12,\,16,\,20$

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. Yes

  2. No

  3. Cannot be determined

  4. None

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Correct Option: A
Explanation:

To check if the set of numbers $ {a,b,c} $are Pythagorean triplets, we need to check if $ {a}^{2} + {b}^{2} = {c}^{2} $

1) For $ {8,15,17} $
$ {8}^{2} + {15}^{2} = 64 + 225 = 289 $
and $ {17}^{2} = 289 $
Hence, $ {8}^{2} + {15}^{2} = {17}^{2} $

2) For $ {16,63,65} $
$ {16}^{2} + {63}^{2} = 256 + 3969 = 4225 $
and $ {65}^{2} = 4225 $
Hence, $ {16}^{2} + {63}^{2} = {65}^{2} $

3)For $ {12,16,20} $
$ {12}^{2} + {16}^{2} = 144 + 256 = 400 $
and $ {20}^{2} = 400 $
Hence, $ {12}^{2} + {16}^{2} = {20}^{2} $

Thus, the given set of numbers are Pythagorean triplets.

Write the Pythagorean triplet whose one member is 30.

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. $226$ and $224$

  2. $220$ and $222$

  3. $227$ and $229$

  4. None of these

Show answer
Correct Option: A
Explanation:

Solution:

General form of pythagorean triplets are $m^2-1,2m,m^2+1$

$\Rightarrow$First member of triplet $a=2m=30\Rightarrow m=15$


Since, it is even 
$\Rightarrow$So, second member of triplet $b=\left(m\right)^2-1=15^2-1=225-1=224$

$\Rightarrow$And third member of triplet $c=m^2+1=225+1=226$

Hence, $A$ is the correct option.

Find the pythagorean triplet.

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. $12,35,37$

  2. $12,36,37$

  3. $12,43,47$

  4. None of these

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Correct Option: A
Explanation:

Every right triangle has side length satisfying:

a$^{2}$ $+$ b$^{2}$ $=$ c$^{2}$
c is the longest side,
Here 
$12^{2}$ $+$ $35^{2}$ $=$ $37^{2}$
Hence it is a pythagorean triplet.
Option A is correct.

A lady went for a walk and she was walking in a right triangular park. The tiles of the smallest side were visible while other 2 sides she couldn't make out. Each tile was 1 m. The length of the visible side was 10 m. Help the lady to find the length of the other 2 sides , so she could calculate what distance she is walking everyday. 

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. 14 m and 16 m

  2. 22 m and 23 m

  3. 24 m and 26 m

  4. 42 m and 46 m

Show answer
Correct Option: C
Explanation:

one side$=10 m$

Other two sides and 10 m should be Pythagorean triplet in order to form right triangle.
$14^{2}$$+$$10^{2}$$=$$296$
$22^{2}$$+$$10^{2}$$=$$584$

$24^{2}$$+$$10^{2}$$=$$576$
$576$$=$$26^{2}$
$42^{2}$$+$$10^{2}$$=$$1864$
Hence, Option C is correct.

Find the pythagorean triplet.

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. $8, 15, 17$

  2. $9, 10, 15$

  3. $9, 10, 17$

  4. None of these

Show answer
Correct Option: A
Explanation:

Every right triangle has side length satisfying:

a$^{2}$ $+$ b$^{2}$ $=$ c$^{2}$
c is the longest side,
Here 
$8^{2}$ $+$ $15^{2}$ $=$ $17^{2}$
Hence it is a pythagorean triplet.
Option A is correct.

Write the Pythagorean triplet whose one member is $24$.

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. $143$ and $145$

  2. $133$ and $144$

  3. $112$ and $115$

  4. $324$ and $325$

Show answer
Correct Option: A
Explanation:

Using  $ 2m, m^2+1, m^2-1$ forms

 Let us take $2m = 24$

$m=\dfrac{24}{2}=12$

if $m = 12, m^2-1=12^2= 144-1 =143$

if $ m = 12, m^2 +1=12^2= 144+1 =145$

Therefore, option A is the correct answer.

Find the Pythagorean triplet whose one member is $18$.

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. $28$ and $20$

  2. $80$ and $82$

  3. $72$ and $92$

  4. $34$ and $54$

Show answer
Correct Option: B
Explanation:

Using  $ 2m, m^2+1, m^2-1$ forms 
Let us take $2m = 18$
           

$m=\dfrac{18}{2}=9$
if $m = 9, m^2-1=9^2= 81-1 =80$
if $ m = 9, m^2 +1=9^2= 81+1 =82$
Therefore, B is the correct answer.

What is the value of x, if (7, x, x - 2) is a Pythagorean triple?

maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

  1. -11.25

  2. 26.5

  3. -16.5

  4. 16.5

Show answer
Correct Option: A
Explanation:

Applying the Pythagorean triples rule as $a^{2}+b^{2}= c^{2}$
$7^{2}+x^{2}= (x - 2)^{2}$
49 + $x^{2}$ = $x^{2}$+ 4 -4x
Both the side $x^{2}$ will get cancelled,
45 = -4x
x = -11.25