Question

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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?
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□ in.

Explanation:

Step1: Set up proportion for similar triangles

Since the triangles are similar, the ratios of corresponding sides are equal. Let \( x \) be the side length of the smaller pennant. So we have the proportion \(\frac{18}{9}=\frac{6}{x}\).

Step2: Cross - multiply to solve for \( x \)

Cross - multiplying gives us \( 18x = 9\times6 \). First, calculate \( 9\times6 = 54 \), so the equation becomes \( 18x=54 \). Then, divide both sides by 18: \( x=\frac{54}{18} \).

Step3: Simplify the fraction

Simplifying \(\frac{54}{18}\) gives us \( x = 3 \).

Answer:

3