Question

Triangle LMN is similar to triangle OPQ. Find the measure of side PQ. Figures are not drawn to scale.

Triangle A = 3 points N M L Small side 36 big side 72 other big side no number

Triangle B = Points Q P O Small side 9.3 other 2 empty

Answer 1

Since LMN ~ OPQ, corresponding vertices are L↔O, M↔P, N↔Q. So MN corresponds to PQ. The given 36 and 72 are sides of LMN, and 9.3 is the corresponding side to 36 in OPQ. The scale factor from LMN to OPQ is 9.3/36.

Thus PQ = 72 * (9.3/36) = 72 * 0.258333... = 18.6.

Answer: PQ = 18.6.