Difference between revisions of "2003 AMC 8 Problems/Problem 6"
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==Problem== | ==Problem== | ||
− | Given the areas of the three squares in the figure, what is the area of the interior triangle? | + | Given the areas of the three squares in the figure, what is the area of the interior triangle? |
+ | |||
+ | <asy> | ||
+ | draw((0,0)--(-5,12)--(7,17)--(12,5)--(17,5)--(17,0)--(12,0)--(12,-12)--(0,-12)--(0,0)--(12,5)--(12,0)--cycle,linewidth(1)); | ||
+ | label("$25$",(14.5,1),N); | ||
+ | label("$144$",(6,-7.5),N); | ||
+ | label("$169$",(3.5,7),N); | ||
+ | </asy> | ||
<math>\mathrm{(A)}\ 13 \qquad\mathrm{(B)}\ 30 \qquad\mathrm{(C)}\ 60 \qquad\mathrm{(D)}\ 300 \qquad\mathrm{(E)}\ 1800</math> | <math>\mathrm{(A)}\ 13 \qquad\mathrm{(B)}\ 30 \qquad\mathrm{(C)}\ 60 \qquad\mathrm{(D)}\ 300 \qquad\mathrm{(E)}\ 1800</math> | ||
Line 8: | Line 15: | ||
The sides of the squares are <math> 5, 12 </math> and <math> 13 </math> for the square with area <math> 25, 144 </math> and <math> 169 </math>, respectively. The legs of the interior triangle are <math> 5 </math> and <math> 12 </math>, so the area is <math> \frac{5 \times 12}{2}=\boxed{\mathrm{(B)}\ 30} </math> | The sides of the squares are <math> 5, 12 </math> and <math> 13 </math> for the square with area <math> 25, 144 </math> and <math> 169 </math>, respectively. The legs of the interior triangle are <math> 5 </math> and <math> 12 </math>, so the area is <math> \frac{5 \times 12}{2}=\boxed{\mathrm{(B)}\ 30} </math> | ||
+ | ==See Also== | ||
{{AMC8 box|year=2003|num-b=5|num-a=7}} | {{AMC8 box|year=2003|num-b=5|num-a=7}} | ||
+ | {{MAA Notice}} |
Latest revision as of 00:47, 5 July 2013
Problem
Given the areas of the three squares in the figure, what is the area of the interior triangle?
Solution
The sides of the squares are and
for the square with area
and
, respectively. The legs of the interior triangle are
and
, so the area is
See Also
2003 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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