The 2 triangles share common vertex upper R.

Common vertex upper R lies on line segment upper P upper T.

Question

$△ Q P R$ is similar to $△ S T R$ . The lengths represented by $\bar{S T}$ , $\bar{Q P}$ , $\bar{P R}$ , and $\bar{Q R}$ in the figure are $14$ , $15$ , $20$ , and $25$ , respectively. What is the length of $\bar{S R}$ ?

Accepted Answer

Choice A is correct. The figure shows that angle P in &#9651; Q P R and angle T in &#9651; S T R are right angles. It follows that angle P is congruent to angle T . The figure also shows that the measures of angle Q R P and angle S R T are both x &#176; . Therefore, angle Q R P is congruent to angle S R T . It&rsquo;s given that &#9651; Q P R is similar to &#9651; S T R . Since angle P is congruent to angle T , and angle Q R P is congruent to angle S R T , it follows that Q R &#175; corresponds to S R &#175; , and Q P &#175; corresponds to S T &#175; . Since corresponding sides of similar triangles are proportional, it follows that S R Q R = S T Q P . It&rsquo;s also given that the lengths of S T &#175; , Q P &#175; , and Q R &#175; are 14 , 15 , and 25 , respectively. Substituting 14 for S T , 15 for Q P , and 25 for Q R in the equation S R Q R = S T Q P yields S R 25 = 14 15 . Multiplying each side of this equation by 25 yields S R = 14 15 25 , or S R = 350 15 . Thus, the length of S R &#175; is 350 15 . Choice B is incorrect. This is the result of solving the equation S R 25 = 14 20 , not S R 25 = 14 15 . Choice C is incorrect. This is the result of solving the equation S R 14 = 15 20 , not S R 25 = 14 15 . Choice D is incorrect. This is the result of solving the equation S R 14 = 15 25 , not S R 25 = 14 15 .

Question 9fe57e