Two corners of an isosceles triangle are at #(1 ,7 )# and #(3 ,3 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

1 Answer
Dec 11, 2017

Measure of the three sides of the triangle are (4.4721, 28.7085, 28.7085)

Explanation:

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Length #a = sqrt((3-1)^2 + (3-7)^2) = sqrt 20 = 4.4721#

Area of #Delta = 64#
#:. h = (Area) / (a/2) = 64 / (4.4721/2) = 64 / 2.2361 = 28.6213#
#side b = sqrt((a/2)^2 + h^2) = sqrt((2.2361)^2 + (28.6213)^2)#
#b = 28.7085#

Since the triangle is isosceles, third side is also #= b = 28.7085#

Measure of the three sides are (4.4721, 28.7085, 28.7085)