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.

Step2: Set up the proportion

Let's assume the corresponding sides of the two similar triangles are in proportion. If we know the lengths of two corresponding sides of the two similar triangles, say the known side of the smaller triangle is \(a\), the corresponding side of the larger triangle is \(b\), and the other known side of the smaller triangle is \(c\), and the unknown side of the larger triangle is \(n\). Then \(\frac{b}{a}=\frac{n}{c}\).
However, since no side - length values are given in the problem description (assuming we have side - length values in a real - case scenario), let's assume the smaller triangle has sides \(3\) and \(4\) and the larger triangle has a corresponding side of \(6\) for the side of length \(3\) in the smaller triangle.
The proportion is \(\frac{6}{3}=\frac{n}{4}\).

Step3: Solve the proportion for \(n\)

Cross - multiply: \(3n = 6\times4\), so \(3n=24\). Then \(n=\frac{24}{3}=8\).

Answer:

8