A right triangle and an isosceles triangle have equal areas. The right triangle has sides of length 3, 4 and 5 units. The isosceles triangle has sides of 3, x and x units. What is the value of x?

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Answer 1 · 2015-11-15T19:12:40

#x = sqrt {73}/2#

Right Triangle 1: basis = 3, height = 4

Triangle 2: basis = 3, height = h

Right Triangle 3: basis = 3/2, height = h, hypotenuse = x

#A = 1/2 cdot 3 cdot 4 = 6 = 1/2 cdot 3 cdot h #

#6 * 2/3 = h = 4#

#x^2 = (3/2)^2 + h^2#

#x^2 = 9/4 + 16 = (9+64)/4#