Example 3: When you have a triangle inside a triangle and 2 of the lines are parallel, the triangles are always similar. You can choose to compare the same "parts of the triangle rather than comparing the whole sides. APQS ATRS​

Answers:

x = 5

y = 3

Explanation:

Triangle PQS has PQ = 12 as the left slanted side. The corresponding left slanted side of the smaller triangle (TRS) is TR = y

The sides PQ and TR form the ratio PQ/TR

The sides QS and RS are the slanted sides on the right of each triangle. They correspond to give the ratio QS/RS. This ratio is equal to the fraction PQ/TR we found earlier.

In this case, QS = QR+RS = 9+3 = 12 and RS = 3

Let's solve for y

PQ/TR = QS/RS

12/y = 12/3

12*3 = y*12 cross multiply

36 = 12y

12y = 36

y = 36/12

y = 3

We'll use the same idea to find x. This time we'll involve the bottom horizontal sides

PS/TS = QS/RS

(15+x)/x = 12/3

3(15+x) = 12x cross multiply

45+3x = 12x

45 = 12x-3x

45 = 9x

9x = 45

x = 45/9

x = 5