How to find the length of the diagonal of a kite - ISEE Upper Level Mathematics Achievement

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Question

A kite has the area of $60\ in^2$ . One of the diagonals of the kite has length $15\ in$ . Give the length of the other diagonal of the kite.

Answer

The area of a kite is half the product of the diagonals, i.e.

$Area=\frac{d_{1}d_{2}}{2}$ ,

where $d_{1}$ and $d_{2}$ are the lengths of the diagonals.

$Area=\frac{d_{1}d_{2}}{2}=\frac{{15}\times {d_{2}}}{2}=60\Rightarrow d_{2}=\frac{60\times 2}{15}\Rightarrow d_{2}=8\ in$

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