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 #1 : How To Find If Trapezoids Are Similar

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 10cm

\displaystyle 9cm

\displaystyle 12cm

\displaystyle 8cm

\displaystyle 11cm

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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