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?

1 Answer
CW
Feb 8, 2017

sqrt145~~12.04√145≈12.04

Explanation:

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

As Area =1/2*b*h=12⋅b⋅h,
where bb is the base and hh is the height.
Here, b=C=18b=C=18
=> 72=1/2*18*h⇒72=12⋅18⋅h
=> h=8⇒h=8

By Pythagorean theorem, we know that
A^2=h^2+(C/2)^2A2=h2+(C2)2
=> A=sqrt(8^2+(18/2)^2)=sqrt145⇒A=√82+(182)2=√145

Hence, A=B=sqrt145~~12.04A=B=√145≈12.04 units

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