Two corners of an isosceles triangle are at #(2 ,4 )# and #(8 ,5 )#. If the triangle's area is #9 #, what are the lengths of the triangle's sides?

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Answer 1 · 2018-05-20T12:10:24

Lengths of three sides are #color(purple)(6.08, 4.24, 4.24#

Given : #A(2,4), B(8,5), Area = 9# and it’s an isosceles triangle. To find the sides of the triangle.

#AB = c = sqrt((8-2)^2 + (5-4)^2) = sqrt37 = 6.08#, using distance formula.

#Area = A_t = 9 = (1/2) * c * h#

#h = (9*2) / sqrt37 = 18 / sqrt37#

Side #a = b = sqrt((c/2)^2 + h^2)#, using Pythagoras theorem

#a = b = sqrt((sqrt37/2)^2 + (18/(sqrt37))^2)#

#=> sqrt((37/4) + (324/37))#

#a = b = 4.24#