An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of $18$ and the triangle has an area of $72$ . What are the lengths of sides A and B?

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Answer 1 · 2017-02-08T07:50:06

$sqrt145~~12.04$

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Given : $A=B, C=18$ , and Area $=72$

As Area $=1/2*b*h$ ,
where $b$ is the base and $h$ is the height.
Here, $b=C=18$
$=> 72=1/2*18*h$
$=> h=8$

By Pythagorean theorem, we know that
$A^2=h^2+(C/2)^2$
$=> A=sqrt(8^2+(18/2)^2)=sqrt145$

Hence, $A=B=sqrt145~~12.04$ units

An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of 18 18 and the triangle has an area of 72 72 . What are the lengths of sides A and B?