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

$Area=\dfrac{1}{2}\times Base\times Height$

$ar(\Delta PQR)=\dfrac{1}{2}\times QR\times PS$

Substituting the given values, we get

$180=\dfrac{1}{2}\times QR\times 15$

$180\times 2=QR\times 15$

$360=QR\times 15$

Divide both sides by 15.

$\dfrac{360}{15}=QR$

$24=QR$

Therefore, the measure of side QR is 24 cm.