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 $16$ $16$ and the triangle has an area of $64$ $64$ . 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 $16$ $16$ and the triangle has an area of $64$ $64$ . What are the lengths of sides A and B?

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Answer 1 · 2016-10-08T02:17:43

$8 \sqrt{2} = 11.3137$ $8sqrt2=11.3137$

Explanation:

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Given $A = B, C = 16$ $A=B, C=16$ , Area $A_{r} = 64$ $A_r=64$ ,

$\Rightarrow A_{r} = \frac{1}{2} \cdot C \cdot h$ $=> A_r=1/2*C*h$
$\Rightarrow 64 = \frac{1}{2} \cdot 16 \cdot h, \Rightarrow h = 8$ $=> 64=1/2*16*h, => h=8$

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

$\Rightarrow A^{2} = 8^{2} + {(\frac{16}{2})}^{2} = 8^{2} + 8^{2} = 128$ $=> A^2=8^2+(16/2)^2=8^2+8^2=128$

$\Rightarrow A = \sqrt{128} = \sqrt{64 \cdot 2} = 8 \sqrt{2} = 11.3137$ $=> A=sqrt128=sqrt(64*2)=8sqrt2=11.3137$

Hence, $A = B = 11.3137$ $A=B=11.3137$

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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 $16$ $16$ and the triangle has an area of $64$ $64$ . What are the lengths of sides A and B?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

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 1616 and the triangle has an area of 6464 . What are the lengths of sides A and B?

1 Answer

Explanation:

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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 $16$ $16$ and the triangle has an area of $64$ $64$ . What are the lengths of sides A and B?