ACT Math : How to find if trapezoids are similar

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #295 : Geometry

Trapezoid A and Trapezoid B are similar. The bases of Trapezoid A are \(\displaystyle 9cm\) and \(\displaystyle 12cm\). Trapezoid B has a smaller base of \(\displaystyle 6cm\). How long is the larger base of Trapezoid B?

Possible Answers:

\(\displaystyle 11cm\)

\(\displaystyle 10cm\)

\(\displaystyle 8cm\)

\(\displaystyle 9cm\)

\(\displaystyle 12cm\)

Correct answer:

\(\displaystyle 8cm\)

Explanation:

Because the two trapezoids are similar, the ratio of their bases must be the same. Therefore, we must set up a cross-multiplication to solve for the missing base:

\(\displaystyle \small \frac{6}{x}=\frac{9}{12}\), using \(\displaystyle \small x\) as the variable for the missing base.

\(\displaystyle \small 72=9x\)

\(\displaystyle \small x=\) \(\displaystyle \small 8\)

Therefore, the length of the longer base of Trapezoid B is \(\displaystyle 8cm\).

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