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 $32$ $32$ . What are the lengths of sides A and B?

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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 $32$ $32$ . What are the lengths of sides A and B?

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Answer 1 · 2016-12-10T02:32:09

$\sqrt{80}$ $sqrt80$

Explanation:

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Area of a triangle $A = \frac{1}{2} \cdot b \cdot h$ $A=1/2*b*h$ , where $b$ $b$ is the base and $h$ $h$ is the height.

Given that $A = B$ $A=B$ , base $C = 8$ $C=8$ , and area of the triangle $= 32$ $=32$ ,
$\Rightarrow 32 = \frac{1}{2} \cdot 8 \cdot h$ $=> 32=1/2*8*h$
$\Rightarrow h = 8$ $=> h=8$

$A^{2} = h^{2} + {(\frac{C}{2})}^{2}$ $A^2=h^2+(C/2)^2$

$\Rightarrow A = \sqrt{8^{2} + {(\frac{8}{4})}^{2}} = \sqrt{80}$ $=> A=sqrt(8^2+(8/4)^2)=sqrt80$

Hence, $A = B = \sqrt{80}$ $A=B=sqrt80$

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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 $32$ $32$ . What are the lengths of sides A and B?

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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 88 and the triangle has an area of 3232 . What are the lengths of sides A and B?

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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 $32$ $32$ . What are the lengths of sides A and B?