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 R T is x. What is the value of x? 12 units 15 units 20 units 25 units

Answer 1

Answer:

RT = 12 units

Step-by-step explanation:

From the figure attached,

ΔSRQ is right triangle.

m∠R = 90°

An altitude has been constructed from point T to side SQ.

m∠RTQ = 90°

By applying geometric mean theorem in triangle SRQ,

$\frac{\text{RT}}{\text{ST}}=\frac{\text{TQ}}{\text{RT}}$

$\frac{x}{9}=\frac{16}{x}$

x² = 16 × 9

x² = 144

x = √144

x = 12

Therefore, length of altitude RT is 12 units.