1956 AHSME Problems/Problem 38
Problem 38
In a right triangle with sides and
, and hypotenuse
, the altitude drawn on the hypotenuse is
. Then:
Solution
The area of this triangle can be expressed in two ways; the first being (as this is a right triangle), and the second being
. But by the Pythagorean Theorem,
. Thus a second way of finding the area of the triangle is
. By setting them equal to each other we get
, and we can observe that the correct answer was
.
~anduran