Question

6. Find QR, if area and altitude PS of ∆PQR are given
ar(∆PQR) = 180 cm2, PS = 15​

Answer 1

Given:

Area and altitude PS of ∆PQR are ar(∆PQR) = 180cm² and PS = 15​.

To find:

The measure of side QR.

Solution:

According to the given information, PS is an altitude of ∆PQR. It means QR is the base of ∆PQR.

We know that, the area of a triangle is

`Area=(1)/(2)* Base* Height`

`ar(\Delta PQR)=(1)/(2)* QR* PS`

Substituting the given values, we get

`180=(1)/(2)* QR* 15`

`180* 2=QR* 15`

`360=QR* 15`

Divide both sides by 15.

`(360)/(15)=QR`

`24=QR`

Therefore, the measure of side QR is 24 cm.