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 # and the triangle has an area of #48 #. 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 # and the triangle has an area of #48 #. What are the lengths of sides A and B?

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Answer 1 · 2016-10-08T18:39:22

#a = b = 10#

Explanation:

Imagine the height of the triangle bisecting side c, thereby, forming two triangles. The area of one of these triangles is 24, its base is 6 and its height can be found using, #A = (1/2)bh#

#24 = (1/2)6h#

#h = 8#

The hypotenuse of this triangle is one of the two equal sides of the original triangle:

#a² = b² = 6² + 8²#

#a² = b² = 100#

#a = b = 10#

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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 # and the triangle has an area of #48 #. What are the lengths of sides A and B?

1 Answer

Explanation:

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