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ISEE Upper Level Math : How to find the length of the diagonal of a kite

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Example Question #51 : Quadrilaterals

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

Possible Answers:

$5\ in$ $\displaystyle 5\ in$

$6\ in$ $\displaystyle 6\ in$

$8\ in$ $\displaystyle 8\ in$

$4\ in$ $\displaystyle 4\ in$

$7\ in$ $\displaystyle 7\ in$

Correct answer:

$8\ in$ $\displaystyle 8\ in$

Explanation:

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

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

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

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

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ISEE Upper Level Math : How to find the length of the diagonal of a kite

Study concepts, example questions & explanations for ISEE Upper Level Math

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Example Question #51 : Quadrilaterals

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