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
[tex]\dfrac{QS}{PS}=\dfrac{RS}{QS}[/tex]
[tex]QS^2=RS\times PS[/tex]
[tex]x^2=18\times (90-18)[/tex]
[tex]x^2=18\times 72[/tex]
[tex]x^2=1296[/tex]
Taking square root on both sides, we get
[tex]x=\sqrt{1296}[/tex]
[tex]x=36[/tex]
Therefore, the correct option is B.
