2007 AMC 8 Problems/Problem 14
Problem
The base of isosceles is
and its area is
. What is the length of one
of the congruent sides?
Solution
The area of a triangle is shown by .
We set the base equal to , and the area equal to
,
and we get the height, or altitude, of the triangle to be .
In this isosceles triangle, the height bisects the base,
so by using the pythagorean theorem, ,
we can solve for one of the legs of the triangle (it will be the the hypotenuse, ).
,
,
The answer is