S Purkayastha Solutions for Chapter: The Triangle and its Properties, Exercise 5: Check Point

With the following numbers, form the Pythagorean triplets.

$12, 13$

A ladder is placed in such a way that its foot is at a distance of 5 m from a wall and its top reaches a window 12 m above the ground. Determine the length of the ladder.

A ladder $25 \mathrm{m}$ long reaches a window of a building $20 \mathrm{m}$ above the ground. Determine the distance of the foot of the ladder from the building.

A man goes $10 \mathrm{m}$ due east and than $24 \mathrm{m}$ due north. Find the distance from the starting point.

Two poles of heights $6 \mathrm{m}$ and $11 \mathrm{m}$ stand on a plane ground. If the distance between their feet is $12 \mathrm{m}$, determine the distance between their tops.

In $△ABC, \angle BCA$ is a right angle, if $Q$ is the mid-point of the side $BC, AC=4 \mathrm{cm}$ and $AQ=5 \mathrm{cm},$ find $(AB{)}^2$.

A right triangle has a hypotenuse of length $p \mathrm{cm}$ and one side of length $q \mathrm{cm}$. If $p-q=1$, find the length of the third side of the triangle.

In following figure, $\angle Q$ and $\angle R$ of $△PQR$ are $25°$ and $65°$ respectively. Write which of the following is true.