Question

a medium and a large triangular bookshelf support made in the same shape are shown. the length n of the missing side in the larger support is ______ inches. (write the answer as a decimal.) the solution is

Explanation:

Step1: Identify similar - triangles property

Since the two triangular bookshelf supports are in the same shape, they are similar triangles. For similar triangles, the ratios of corresponding sides are equal.
Let's assume the ratio of the sides of the smaller triangle to the larger triangle is the same for all corresponding sides. If we assume the side of length 6 inches in the smaller triangle corresponds to the side of length 9 inches in the larger triangle, and the side of length 12 inches in the smaller triangle corresponds to the side of length $n$ inches in the larger triangle.
The ratio of the sides of the two similar triangles is $\frac{9}{6}=\frac{3}{2}$.

Step2: Set up proportion

We set up the proportion $\frac{n}{12}=\frac{9}{6}$.
Cross - multiply: $6n = 12\times9$.

Step3: Solve for $n$

First, calculate $12\times9 = 108$. Then, we have $6n=108$.
Divide both sides by 6: $n=\frac{108}{6}=18.0$.

Answer:

$18.0$