Length of the diagonal - class-X
Description: length of the diagonal | |
Number of Questions: 47 | |
Created by: Shaka Gupte | |
Tags: mensuration maths surface area and volume surface area and volume of cube and cuboid trigonometrical ratio and identities |
If the measures of the sides of a triangle are ________, then it is not a right angled triangle.
Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved the distance equal to half of the longer side. Then the ratio of the shorter side to the longer side is?
$\angle B$ is a right angle is in $\Delta ABC$v and P,Q are points of trisection of hypotenuse $\bar{AC}.$ then $BP^{2}+BQ^{2}=\frac{5}{9}AC^{2}.$
In $\triangle ABC$ right angled at $B, AB=5\ cm$ and $\angle ACB=30^{o}$ then the length of the sides $BC$ is
ABC is a triangle, right-angled at B. M is a point on BC. Hence,
$AM^{2}\, +\, BC^{2}\, =\, AD^{2}\, +\, BM^{2}$
State true or false.
A guy wire attached to a vertical pole of height $18m$ is $24m$ long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
The sides of a rectangular field are $80$ m and $18$ m respectively. The length of the diagonal is:
A person wishes to fit three rods together in the shape of a right-angled triangle so that the hypotenuse is to be $4:cm$ longer than the base and $8:cm$ longer than the altitude. The lengths of the rods are:
What is the value of the hypotenuse of a right triangle whose sides are $12$ and $18$?
A triangle whose lengths of sides are $5$ cm, $12$ cm and $13$ cm. The triangle is ____________.
In any triangle $ABC$, $AB^{2} + AC^{2} = 3 (AO^{2} + OC^{2})$.
where $O$ is mid-point of $BC$.
Two cars are travelling along two roads which cross each other at right angles at $A$. One car is travelling towards A at $21\ kmph $ and the other is travelling towards $A$ at $28\ kmph$.If initially, their distance from $A$ are $1500\ km$ and $2100\ km$ respectively,then the nearest distance between them is ,
The perpendicular from A on side BC of a $\Delta ABC$ intersects BC at D such that $DB = 3CD$, then $2A{B^2} = A{C^2} + B{C^2}$.
then $BP^2 + CQ^2=5PQ^2$
In a quadrilateral ABCD, $\angle B\, =\, 90^{\circ}$ and $\angle D\, =\, 90^{o}$. Then:
A grassy land in the shape of a right angled triangle has its hypotenuse $1$ metre more than twice the shortest side. If the third side is $7$ metres more than the shortest side. The sides of the grassy land are:
The hypotenuse of a right angled triangle is $25$cm. The other two sides are such that one is $5$cm longer than the other. Their lengths (in cm) are:
Hypotenuse of a right triangle is $25cm$ and out of the remaining two sides, one is longer than the other by $5cm$. Find the lengths of the other two sides.
The lengths of the sides of a right-angled triangle are all given in natural numbers. If two of these numbers are odd and they differ by $50$, then the least possible value for the third side is:
The distance between the top of two trees $20$m and $28$m high is $17$m. The horizontal distance between the trees is:
One side other than the hypotenuse of a right-angled isosceles triangle is $4$ cm. The length of the perpendicular on the hypotenuse from the opposite vertex is:
The length of the hypotenuse of a right angled $\Delta$ whose two legs measure $12 \ cm$ and $0.35 \ m$ is:
In a $\Delta ABC,\,AB=AC=2.5\;cm,\,BC=4\;cm$. Find its height from $A$ to the opposite base.
If the sum of the length, breadth and depth of a cuboid is S and its diagonal is d, then its surface is _____________.
In $\Delta$ABC, $\angle B = 90^{o}, AB = 8 \ cm$ and $BC = 6 \ cm.$ The length of the median $BM$ is:
If the sides of a right angled triangle are $x, 3x + 3$ and $3x + 4$, then $x$ is equal to:
In a field of shape of a right angled triangle, the farmer wants to measure the $3$ sides but being a huge field, he was only able to measure $2$ sides, $1$ side of which was $6$ km and other was $8$ km. Can you find the length of $3^{rd}$ side for him?
If the Pythagorean triples of one member is $10$, find the other two members.
If the Pythagorean triples of one member is $8$, find the other two members.
If the Pythagorean triples of one member is $22$, find the other two members.
Which of the following can't be the lengths of the sides of a right-angled triangle?
The ratio of the two legs of a right-angled triangle is $3:1$. If the lengths of the legs are whole numbers, what can be the possible value of the hypotenuse?
A man goes $12$ miles due east and then $9$ miles due north. Calculate the distance travelled, if he takes the theoretically shortest path.
A boat travels $10$ miles East and then $24$ miles South to an island. How many miles are there from the point of departure of the boat to the island?
Sheila leaves her house and starts driving due south for $30$ miles, then drives due west for $60$ miles, and finally drives due north for $10$ miles to reach her office. Find her approximate displacement.
$\angle B$ in $\triangle ABC$ and $\angle S$ in $\triangle RST$ are right angles. The lengths of sides $AC$ and $RT$ are equal. Determine the relation between the following.
The sides of a triangle are $25 m$, $39 m$ and $56 m$ respectively. Find the length of perpendicular from the opposite angle on the greatest sides.
In $\triangle ABC,\angle ABC={ 90 }^{ o }$. If $AC=(x+y)$ and $BC=(x-y)$, then the length of $AB$ is:
A pilgrim started from a shrine. After walking straight for $100 m$, he moved to his right and then after $500 m$, he again moved to his right. After walking a distance of $100 m$, he moved to his left and then walked $200 m$. He again moved to his right and walked $700 m$.
What is the distance of his location from the shrine?
$PQ$ is the diameter of a semicircle with radius $4\ cm$ and $\angle PRQ$ is the angle on the semicircle. If $QR = 2\sqrt {7} cm$, then length of $PR$ is :
In a triangle $ABC$ with $\angle A = 90^o$, $P$ is a point on $BC$ such that $PA : PB = 3:4$. If $AB=\sqrt{7}$ and $AC=\sqrt{5}$, then $BP:PC$ is
Triangle $ABC$ is right angled at $A$. The points $P$ and $Q$ are on the hypotenuse $BC$ such that $BP = PQ = QC$.
If $AP = 3$ and $AQ = 4$, then the length $BC$ is equal to
Given that in a right angled triangle the length of two sides are 11 and 60. Find the perimeter of the triangle.
In a right angled triangle the hypotenuse is $2\sqrt{2}$ times the length of the perpendicular drawn from the opposite vertex on the hypotenuse. The the other two angles are
In a right angled triangle, the square of the hypotenuse is equal to twice the product of the other two sides. One of the acute angles of the triangle is:
Evaluate cos$\begin{pmatrix}2csc^{-1}(\dfrac{x+4}{5})\end{pmatrix} = $
Diagonals $\overline{AC}$ and $\overline{BD}$ of quadrilateral $ABCD$ are perpendicular. $AD=DC=8, AC=BC=6, m\angle ADC = 60^o$. The area of $ABCD$ is