Question

COLOR THEME

Q ZOOM
7. The dimensions in the drawing below are given in units.
3V10
х
36
Р
118
S
R
90
18V5
What is the value of x?
45
CLEAR ALL

Answer 1

Given:

In triangle PQR, QS⊥PR, QS=x, PR=90 and RS=18.

To find:

The value of x.

Solution:

According to right triangle altitude theorem (geometric mean theorem), if an altitude of a right triangle divides the base into two segments then the square of altitude is equal to the product segments of the base.

Using right triangle altitude theorem, we get

`(QS)/(PS)=(RS)/(QS)`

`QS^2=RS* PS`

`x^2=18* (90-18)`

`x^2=18* 72`

`x^2=1296`

Taking square root on both sides, we get

`x=√(1296)`

`x=36`

Therefore, the correct option is B.