Question

Triangles ABC and PQR are shown http://img.ctrlv.in/4e235b954dc5d.jpg. The
given side lengths are in centimeters. The area of
ABC is 30 square centimeters. What is the area of
PQR, in square centimeters?
ACT Practice, answer is 30, I just don't know why.

Answer 1

http://img.ctrlv.in/img/4e235b954dc5d.jpg

Answer 2

are "x" and "y" equal to each other?

Answer 3

It doesn't say

Answer 4

You can assume that x,y are equal in both triangles because they have the same name.


Area of this triangle is
$$
A={1\over2}xy\sin \theta
$$
So for the 1st triangle
$$
A_1={1\over2}xy\sin \theta=30\\
xy={2\times 30\over\sin 70}
$$
For the second, using the results for \(xy\):
$$
A={1\over2}xy\sin {110}={1\over2}\times {2\times 30\over\sin 70}\sin 110=30
$$
see - http://en.wikipedia.org/wiki/Triangle#Using_trigonometry

Answer 5

Does this make sense?

Answer 6

Yes, thank you!