Question

a sporting goods store sells triangular team pennants in two sizes. the base of one pennant is 18 in. and the length of the side is 9 in. the other pennant is similar to the larger pennant and has a base that is 6 in. what is the length of the side of the smaller pennant? enter your answer in the box.

Explanation:

Step1: Recall similar triangles property

For similar triangles, the ratios of corresponding sides are equal. Let the length of the side of the smaller pennant be \( x \) inches. The ratio of the bases of the two pennants is equal to the ratio of their corresponding sides. So we can set up the proportion: \(\frac{\text{Base of larger pennant}}{\text{Base of smaller pennant}}=\frac{\text{Side of larger pennant}}{\text{Side of smaller pennant}}\)

Step2: Substitute the known values

We know the base of the larger pennant is 18 in, the base of the smaller is 6 in, and the side of the larger is 9 in. Substituting these values into the proportion: \(\frac{18}{6}=\frac{9}{x}\)

Step3: Solve for \( x \)

First, simplify \(\frac{18}{6}=3\), so the equation becomes \( 3=\frac{9}{x} \). Cross - multiply to get \( 3x = 9 \). Then divide both sides by 3: \( x=\frac{9}{3}=3 \)

Answer:

3