ACT Math : How to find the length of the diagonal of a rhombus

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #11 : How To Find The Length Of The Diagonal Of A Rhombus

If the area of a rhombus is \(\displaystyle 60\:cm^2\), and the length of one of its diagonals is \(\displaystyle 2\:cm\), what must be the length of the other diagonal?

Possible Answers:

\(\displaystyle 45\:cm\)

\(\displaystyle 90\:cm\)

\(\displaystyle 30\:cm\)

\(\displaystyle 60\:cm\)

\(\displaystyle 120\:cm\)

Correct answer:

\(\displaystyle 60\:cm\)

Explanation:

Write the formula for the area of a rhombus.

\(\displaystyle A=\frac{d_1\cdot d_2}{2}\)

Plug in the given area and diagonal length. Solve for the other diagonal.

\(\displaystyle 60\:cm^2=\frac{2\:cm\cdot d_2}{2}\)

\(\displaystyle 2(60\:cm^2)=2(\frac{2\:cm\cdot d_2}{2})\)

\(\displaystyle 120\:cm^2=2\:cm\cdot d_2\)

\(\displaystyle \frac{120\:cm}{2\:cm}=\frac{2\:cm\cdot d_2}{2\:cm}\)

\(\displaystyle d_2 =60\:cm\)

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