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

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Answer 1 · 2018-03-08T12:00:43

Side #color(brown)(a = b = 16.49# units

A median if triangle divides it in 2 triangles of equal areas. And if it is isosceles triangle the median is perpendicular bisector.

#c = 8 #

#a = b, height = h#

Half base = c / 2 = 8 / 2 = 4

Area of triangle = 64 sq units

Area of half triangle = 32 sq units

1/2 * 4 * h = 32

#height# #h = 16 # units

By using Pythagoras theorem

#a = b = sqrt(4^2 + 16^2) = sqrt 272 = color(brown)(16.49# units

Answer 2 · 2018-03-08T12:13:27

#A = B = 4sqrt 17 "units"#

Let # h # the height#

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#"area of triangle" = 1/2 xxh xxC#
#64 = 1/2 xx h xx8#
#h = 16 " units"#

#∆ MHN: #
#MN^2 = h^2 + NH^2 #
#A^2 = 16^2 + (8/2)^2#
#A = sqrt 272#
#A = 4sqrt 17 #

#A = B = 4sqrt 17 "units"#