2003 AMC 8 Problems/Problem 6

Problem 6

Given the areas of the three squares in the figure, what is the area of the interior triangle?

$\mathrm{(A)}\ 13 \qquad\mathrm{(B)}\ 30 \qquad\mathrm{(C)}\ 60 \qquad\mathrm{(D)}\ 300 \qquad\mathrm{(E)}\ 1800$

Solution

The sides of the squares are $5, 12$ and $13$ for the square with area $25, 144$ and $169$ , respectively. The legs of the interior triangle are $5$ and $12$ , so the area is $\frac{5 \times 12}{2}=\boxed{\mathrm{(B)}\ 30}$

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2003 AMC 8 Problems/Problem 6

Problem 6

Solution