Jagat Jitendra Matto Solutions for Chapter: The Triangle and Its Properties, Exercise 3: EXERCISE 12.3

The hypotenuse of a right-angled triangle is $25 \mathrm{cm}$. If one of the remaining two sides is $15 \mathrm{cm}$, find the length of its third side.

A man goes $10 \mathrm{m}$ due east and then $24 \mathrm{m}$ due north. How far is he from the starting point?

The sides of a triangle are $15 \mathrm{cm}, 36 \mathrm{cm}$ and $39 \mathrm{cm}$. Verify that it is a right-angled triangle.

A ladder $4.5 \mathrm{m}$ long is placed against a wall in such a way that the foot of the ladder is $2.7 \mathrm{m}$ away from the wall. Find the height of the wall to which the ladder reaches.

Two poles of heights $9 m$ and $14 m$ stand upright on a plane ground. If the distance between their feet is $12 m$, The distance between their tops $x m$ . Find the value of $x$?

The sides of a triangle are of lengths $6.5 \mathrm{cm}, 6 \mathrm{cm}$ and $2.5 \mathrm{cm}$. Is this triangle a right triangle? If so, which is the hypotenuse?

The adjacent sides of a rectangle are $3.6 \mathrm{cm}$ and $1.5 \mathrm{cm}$. Find the length of the diagonal. 

$\mathrm{ABC}$ is an isosceles right triangle, right angled at $\mathrm{C}$. Prove that ${\mathrm{AB}}^2= 2{\mathrm{AC}}^2$.