An isosceles right triangle has a perimeter of 94 + 94 2 inches. What is the length, in inches, of

Question

An isosceles right triangle has a perimeter of 94 + 94 2 inches. What is the length, in inches, of one leg of this triangle?

Accepted Answer

Choice B is correct. It's given that the right triangle is isosceles. In an isosceles right triangle, the two legs have equal lengths, and the length of the hypotenuse is 2 times the length of one of the legs. Let l represent the length, in inches, of each leg of the isosceles right triangle. It follows that the length of the hypotenuse is l 2 inches. The perimeter of a figure is the sum of the lengths of the sides of the figure. Therefore, the perimeter of the isosceles right triangle is l + l + l 2 inches. It's given that the perimeter of the triangle is 94 + 94 2 inches. It follows that l + l + l 2 = 94 + 94 2 . Factoring the left-hand side of this equation yields 1 + 1 + 2 l = 94 + 94 2 , or 2 + 2 l = 94 + 94 2 . Dividing both sides of this equation by 2 + 2 yields l = 94 + 94 2 2 + 2 . Rationalizing the denominator of the right-hand side of this equation by multiplying the right-hand side of the equation by 2 - 2 2 - 2 yields l = 94 + 94 2 2 - 2 2 + 2 2 - 2 . Applying the distributive property to the numerator and to the denominator of the right-hand side of this equation yields l = 188 - 94 2 + 188 2 - 94 4 4 - 2 2 + 2 2 - 4 . This is equivalent to l = 94 2 2 , or l = 47 2 . Therefore, the length, in inches, of one leg of the isosceles right triangle is 47 2 . Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect. This is the length, in inches, of the hypotenuse. Choice D is incorrect and may result from conceptual or calculation errors.

Question an-iso