Question

What is the value of x? x= units

Answer 1

By Pythagoras theorem

$RQ^{2}= x^{2} + 16^{2}$
$RS^{2}= x^{2} + 9^{2}$

$SQ^{2}= RS^{2} + RQ^{2}$
$SQ^{2}= x^{2} + 16^{2} + x^{2} + 9^{2}$
$SQ^{2}=2 x^{2} +256+81$
$25^{2}=2 x^{2} +337$
$625-337=2 x^{2}$
$288=2 x^{2}$
$144= x^{2}$
$x=12$

Answer 2

Answer:  The value of x is 12 units.

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

We can see that triangle RSQ is a right-angled one with m∠SRQ = 90°. And RT is perpendicular to the hypotenuse SQ.

Given ST = 9 units, TQ = 16 units  and  RT = x = ?

Since ΔRSQ is a right-angled triangle with hypotenuse SQ and RT is perpendicular to SQ, so we must have

$RT^2=ST\times TQ\\\\\Rightarrow x^2=9\times 16\\\\\Rightarrow x^2=144\\\\\Rightarrow x=\pm \sqrt{144}\\\\\Rightarrow x=\pm12.$

Since the length of a line segment cannot be negative, so the value of of x is 12 units.

Thus, the required value of x is 12 units.