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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