Question

(GEOMETRY E2020) What is the value of X?

Answer 1

Answer:  The required value of x is 12.

Step-by-step explanation:  We are given to find he value of x fro the figure shown.

We note from the figure that

triangle RSQ is aright-angled one, where

∠SRQ=90°, ST = 9, QT = 16  and  RT is the altitude drawn to the hypotenuse SQ.

We know that

if an altitude is drawn from the right-angle of a right-angled triangle to the hypotenuse, then the square of the altitude is equal to the product of the two segments of the hypotenuse.

So, in the given right-angled triangle RSQ, we get

$RT^2=ST \times TQ\\\\\Rightarrow x^2=9\times 16\\\\\Rightarrow x^2=144\\\\\Rightarrow x=\pm\sqrt{144}\\\\\Rightarrow x=\pm 12.$

Since length of a side cannot be negative, so x = 12.

Thus, the required value of x is 12.

Answer 2

Use the formula $h^{2} =xy$ so:
$x^{2} =9(16)$
$x^{2} =144$
$\sqrt{ x^{2} } = \sqrt{144}$
$x=12$