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Two corners of an isosceles triangle are at #(2 ,4 )# and #(3 ,8 )#. If the triangle's area is #18 #, what are the lengths of the triangle's sides?

Answer 1

Avery Allen

First find the length of the base, then solve for the height using the area of 18.

Using the distance formula ...

length of base #=sqrt[(3-2)^2+(8-4)^2]=sqrt17#

Next, find the height ...

Triangle Area = #(1/2) xx("base")xx("height")#

#18=(1/2)xxsqrt17xx("height")#

height #=36/sqrt17#

Finally, use Pythagorean theorem to find the length of the two equal sides ...

#(height)^2+[(1/2)(base)]^2=(side)^2#

#(36/sqrt17)^2+[(1/2)(sqrt17)]^2=(side)^2#

Sides #=sqrt(5473/68)~~8.97#

In summary, the isosceles triangle has two equal sides of length #~~8.97# and a base length of #sqrt17#

Hope that helped

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Answer 2

Sadie Adams

The lengths of the triangle's sides are approximately 6 units each.

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