Question

multiple choice 4 points
2
two triangles are similar. the measure of the shortest side of the first triangle is 12
and the measure of the shortest side of the second triangle is 5. if the longest side
of the first triangle measures 15, what is the measure of the longest side of the
second triangle?
24
36
6.25
2.4

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let \(x\) be the longest side of the second triangle. The proportion is \(\frac{\text{shortest side of first}}{\text{shortest side of second}}=\frac{\text{longest side of first}}{\text{longest side of second}}\), so \(\frac{12}{5}=\frac{15}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(12x = 5\times15\).

Step3: Solve for \(x\)

\(12x=75\), then \(x=\frac{75}{12}=6.25\).

Answer:

\(6.25\)