Question

Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9 and the length of T Q is 16. The length of S R is x. What is the value of x? 12 units 15 units 20 units 24 units

Answer 1

Answer:

edge says C is correct

Step-by-step explanation:

Answer 2

Answer:

Option B.

Step-by-step explanation:

It is given that ΔSRQ is a right angle triangle, ∠SRQ is right angle.

RT is altitude on side SQ, ST=9, TQ=16 and SR=x.

In ΔSRQ and ΔSTR,

$m\angle S=m\angle S$           (Reflexive property)

$m\angle R=m\angle T$           (Right angle)

By AA property of similarity,

$\triangle SRQ\sim \triangle STR$

Corresponding parts of similar triangles are proportional.

$\dfrac{SR}{SQ}=\dfrac{ST}{SR}$

Substitute the given values.

$\dfrac{x}{9+16}=\dfrac{9}{x}$

$\dfrac{x}{25}=\dfrac{9}{x}$

On cross multiplication we get

$x^2=25\times 9$

$x^2=225$

Taking square root on both sides.

$x=\sqrt{225}$

$x=15$

The value of x is 15. Therefore, the correct option is B.