2006 iTest Problems/Problem 22
Problem
Triangle has sidelengths , , and . Point is the foot of the altitude from , and lies on segment such that . Find the area of the triangle .
Solution
Note that because the area of a triangle is the same, the product of the right triangle's legs equals the hypotenuse multiplied by the altitude to the hypotenuse. Thus, we have , so . We also have , so .
By the Pythagorean Theorem, . Therefore, the area of triangle equals .
See Also
2006 iTest (Problems, Answer Key) | ||
Preceded by: Problem 21 |
Followed by: Problem 23 | |
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