Question

Why is the value of q?

Answer 1

Given:

QSR is a right triangle.

QT = 10

TR = 4

To find:

The value of q.

Solution:

Hypotenuse of QSR = QT + TR

                                 = 10 + 4

                                 = 14

Geometric mean of similar right triangle formula:

$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text { leg }}{\text { part }}$

$\Rightarrow \frac{14}{q} =\frac{q}{4}$

Do cross multiplication.

$\Rightarrow14\times 4 =q\times q$

$\Rightarrow 56 =q^2$

Switch the sides.

$\Rightarrow q^2 =56$

Taking square root on both sides.

$\Rightarrow q =2 \sqrt{14}$

The value of q is $2 \sqrt{14}$.