Question

In the figure below, triangle RPQ is similar to triangle RTS.

Triangle R P Q. Side P R is 42 and side P Q is x. Triangle S R T. Side S T is 36 and side R T is 28.

What is the distance between P and Q?
24
42
50
54


answer D.

Answer 1

the correct answer must be 54, but your problem description was not clear defining what corner (letter) of what triangle corresponds to what corner (letter) of the other. but by deduction of what it cannot be, 54 remains.

Explanation:

the most likely problem interpretation :

is 42 (of RPQ) the longer or shorter side (compared to 36 and 28 of STR) ?

since the triangle are similar, their angles must be the same, and the side lengths of both triangles must have a constant factor in their relation to each other.

first assumption : 42 is the longer side of RPQ.

then the solution could only be 24 (the only solution option smaller than 42). then 42 must be of the same relation to 36, as 24 is to 28. which is wrong, because 42 is bigger than 36, but 24 is smaller than 28.

so, second assumption, 42 is the shorter side of RPQ.

then 42 is in the same relation to 28, as x is to 36.

so, 42/28 = x/36.

=> 42/7 = x/9

=> 6 = x/9

=> 6*9 = x = 54