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 8 8 and the triangle has an area of 88 88. What are the lengths of sides A and B?

1 Answer
Alan P.
Jun 10, 2016

abs(A)=abs(B)=10sqrt(5)|A|=|B|=10√5

Explanation:

Viewing C as the base and denoting the height as hh
the formula for the area of a triangle tell us that:
color(white)("XXX")1/2*8*h=88XXX12⋅8⋅h=88 (using the given values)

This implies that h=22h=22

Side A (or B) together with half the length of C and the height form a right-angled triangle (with A the hypotenuse).

Therefore
color(white)("XXX")abs(A)=sqrt(4^2+22^2)=sqrt(500)=10sqrt(5)XXX|A|=√42+222=√500=10√5

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