An isosceles right triangle has a hypotenuse of length 58 inches. What is the perimeter, in inches, of this triangle?

Question

Accepted Answer

Choice C is correct. Since the triangle is an isosceles right triangle, the two sides that form the right angle must be the same length. Let x be the length, in inches, of each of those sides. The Pythagorean theorem states that in a right triangle, a 2 + b 2 = c 2 , where c is the length of the hypotenuse and a and b are the lengths of the other two sides. Substituting x for a , x for b , and 58 for c in this equation yields x 2 + x 2 = 58 2 , or 2 x 2 = 58 2 . Dividing each side of this equation by 2 yields x 2 = 58 2 2 , or x 2 = 2 /mo> 58 2 4 . Taking the square root of each side of this equation yields two solutions: x = 58 2 2 and x = - 58 2 2 . The value of x must be positive because it represents a side length. Therefore, x = 58 2 2 , or x = 29 2 . The perimeter, in inches, of the triangle is 58 + x + x , or 58 + 2 x . Substituting 29 2 for x in this expression gives a perimeter, in inches, of 58 + 2 29 2 , or 58 + 58 2 . Choice A is incorrect. This is the length, in inches, of each of the congruent sides of the triangle, not the perimeter, in inches, of the triangle. Choice B is incorrect. This is the sum of the lengths, in inches, of the congruent sides of the triangle, not the perimeter, in inches, of the triangle. Choice D is incorrect and may result from conceptual or calculation errors.

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