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# A square piece of paper is folded once so that one pair of opposite corners coincide

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A square piece of paper is folded once so that one pair of opposite corners coincide. When the paper is unfolded, two congruent triangles have been formed. Given that the area of the original square is 64 square inches, what is the number of inches in the perimeter of one of these triangles? Express your answer in simplest radical form.

Nov 3, 2020

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If the area of the original square is $$64$$ square inches, then the perimeter is $$32$$ inches, and each side is $$8$$ inches. Each triangle will have an area of $$32$$ square inches. The perimeter of the triangles is $$16$$ + the hypotenuse. The length of the hypotenuse is given by the Pythagorean theorem: $$a^2 + b^2 = c^2$$ so we have $$8^2 + 8^2 = c^2$$ therefore the length of the hypotenuse is $$\sqrt{128}$$  so your answer is $$16 + \sqrt{128} = 16 + 8\sqrt{2}$$

I'm not 100% sure this is the answer you want, if you need anything else, just ask :D

Nov 3, 2020
edited by SqltyPi  Nov 3, 2020