triangle PQS

In ΔPQS above, if PQ =3 and PS = 4, then PR = ?

(A) 9/4
(B) 12/5
(C) 16/5
(D) 15/4
(E) 20/3

Highlight to see answer: B

Please post your explanations in the comments below!

One Response to “Triangle PQS”

Ivan says:

This is more of a POE solution that uses knowledge that we have about Triangles and the Pythagorean theorem:

PR is what we are looking for and PR is a side of Triangle PRS. So what do we know about Triangle PRS??? Triangle PRS is a 45, 45, 90 triangle because <PRS is 90deg. and <RPS is 45deg because it bisects a 90deg angle. so <RSP must be 45deg. In a 45-45-90 triangle the sides are in 1:1: sqrt 2 proportion. side PS is our hypotenuse because it is the side across from the largest angle (90deg) so using the Pythagorean theorem a^2 + b^2 = c^2 we know that side PR and RS are equal and the hypotenuse(4) will be 4^2=16. so PR^2 + RS^2 = 16 and since PR and RS are equal then they both must represent sqrt of 8 because 8+8=16 according to the Pythagorean theorem so…..

Which one of your answers most closely represents sqrt of 8???? sqrt of 8 is somewhere between 2.5 and 3 so you just run the improper fractions in the answers and change them to mixed numbers to more easily identify which one is closer to 2.53. 12/5 is the closer answer so B is the correct answer!!!!

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