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 # and the triangle has an area of #72 #. 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 # and the triangle has an area of #72 #. What are the lengths of sides A and B?

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Answer 1 · 2016-10-14T07:16:25

12.04(approx)

Explanation:

Let the length of side A or B = x and base is 16. So the height is #sqrt [x^2 - (16/2)^2]#
Now the area of triangle = 1/2 * base * height
= # 1/2 * 16 * sqrt[x^2 - (16/2)^2]#.
Therefore,
#1/2 * 16 * sqrt[x^2 - (16/2)^2]# = 72
or, #sqrt[x^2 - 8^2]=72/8#
or, #x^2# - 64 = 81
or, #x^2# = 145
or, x = #sqrt 145# = 12.04 (approx)

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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 # and the triangle has an area of #72 #. What are the lengths of sides A and B?

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Explanation:

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