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

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Question

If the area of a rhombus is , and the length of one of its diagonals is , what must be the length of the other diagonal?

Answer

Write the formula for the area of a rhombus.

$A=\frac{d_1\cdot d_2}{2}$

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

$60:cm^2=\frac{2:cm\cdot d_2}{2}$

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

$120:cm^2=2:cm\cdot d_2$

$\frac{120:cm}{2:cm}=\frac{2:cm\cdot d_2}{2:cm}$

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