Question

The triangles are similar.

What is the value of x?


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(please give an explaination for how you got the answer so i can understand it)

Answer 1

Answer: x = 12

The triangles are similar, so the corresponding sides on each triangle can be turned into ratios

(4x + 12)/(15) = (32)/(8) (ratios)
(8(4x + 12))/120 = (32)(15)/120 (multiple denominators to make them equal)

(32x + 96)/120 = 480/120 (distribute)
32x + 96 = 480 (forget the denominators since they’re the same now)

32x = 384 (subtract 96 from both sides)
x = 12 (divide both sides by 32