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 $12$ $12$ and the triangle has an area of $81$ $81$ . 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 $12$ $12$ and the triangle has an area of $81$ $81$ . What are the lengths of sides A and B?

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Answer 1 · 2016-03-24T22:32:51

I found $14.77$ $14.77$

Explanation:

Consider the diagram:
enter image source here
The Area is given as:

$Area = \frac{Base \times Height}{2} \frac{C \times H}{2} = 81$ $"Area"=("Base"xx"Height")/2(CxxH)/2=81$

So:

$\frac{12 \cdot H}{2} = 81$ $(12*H)/2=81$
$H = \frac{81}{6} = 13.5$ $H=81/6=13.5$

We use half triangle and Pythagoras:

$A^{2} = H^{2} + {(\frac{C}{2})}^{2} = H^{2} + \frac{C^{2}}{4} = {13.5}^{2} + \frac{12^{2}}{4} = 182.25 + 36 = 218.25$ $A^2=H^2+(C/2)^2=H^2+C^2/4=13.5^2+12^2/4=182.25+36=218.25$

and:

$A = \sqrt{218.25} = 14.77 = B$ $A=sqrt(218.25)=14.77=B$

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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 $12$ $12$ and the triangle has an area of $81$ $81$ . 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 12 1212 and the triangle has an area of 81 8181 . 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 $12$ $12$ and the triangle has an area of $81$ $81$ . What are the lengths of sides A and B?