Question

1. the ratio of the side lengths for a triangle is exactly 12:14:15. in a second triangle similar to the first, the shortest side is 8 inches long. to the nearest tenth of an inch, what is the length of the longest side of the second triangle? a. 11.0 b. 10.0 c. 9.3 d. 6.4 e. cannot be determined from the given information

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let the length of the longest side of the second triangle be $x$. The ratio of the shortest to the longest side in the first triangle is $\frac{12}{15}$, and in the second triangle is $\frac{8}{x}$. So we have the proportion $\frac{12}{15}=\frac{8}{x}$.

Step2: Cross - multiply

Cross - multiplying gives us $12x = 15\times8$.

Step3: Solve for $x$

First, calculate $15\times8 = 120$. Then, $x=\frac{120}{12}=10.0$.

Answer:

B. 10.0