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?

a. 12 units
b. 15 units
c. 20 units
d. 24 units

Answer 1

Answer:

Option b.

Step-by-step explanation:

Given : $\Delta SRQ$ is right angled triangle . 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.

In the figure, $\angle SRQ=90^{\circ}$ and RT is perpendicular to SQ.

We know that in a right angled triangle if a perpendicular is drawn from the vertex of the right angle to the hypotenuse then triangles on both sides of the perpendicular are similar to each other and to the whole triangle .

Therefore , $\Delta STR\sim \Delta SRQ$

Also, we know that if two triangles are similar then their sides are proportional .

$\frac{ST}{SR}=\frac{SR}{SQ}\\\frac{9}{x}=\frac{x}{25}\\x^2=25\times 9\\x=5\times 3\\=15$

So, option b. is correct

Answer 2

Answer:

The correct answer is B. 15 units