Question

Math Help!!! Can someone please solve this?? I will give you Brainliest!

Answer 1

Triangles PQR and PSR are right triangles, with both QR = SR = 5 (since these are radii of the circle R).

TR is also a radius of the circle, so TR = 5, making PR = 4 + TR = 9.

Because PQR and PSR are right triangles, we can compute the length of the missing side, which will be equal. By the Pythagorean theorem,

PQ^2 + QR^2 = PR^2

PQ^2 + 5^2 = 9^2

PQ^2 = 56

PQ = √56 = 2√14

Then the perimeter of PQRS is

PQ + QR + RS + SP = 2√14 + 5 + 5 + 2√14 = 10 + 4√14

and so the answer is B.