Difference between revisions of "2007 AMC 8 Problems/Problem 14"
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we can solve for one of the legs of the triangle (it will be the the hypotenuse, <math>c</math>). | we can solve for one of the legs of the triangle (it will be the the hypotenuse, <math>c</math>). | ||
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+ | <math>a = 12</math>, <math>b = 5</math>, | ||
<math>c = 13</math> | <math>c = 13</math> | ||
The answer is <math>\boxed{C}</math> | The answer is <math>\boxed{C}</math> |
Revision as of 17:10, 26 March 2010
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