Question

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

A) 29√2
B) 58√2
C) 58+58√2
D) 58+116√2

Answer 1

To find the perimeter of an isosceles right triangle with a hypotenuse of 58 inches, we use the Pythagorean theorem to find the legs and then add them to the hypotenuse. The correct perimeter is 58 + 58√2 inches, which corresponds to answer choice C.

Step-by-step explanation:

The question is asking us to determine the perimeter of an isosceles right triangle when only the hypotenuse is given. In an isosceles right triangle, the lengths of the two legs are equal. Using the Pythagorean theorem (a² + b² = c²), and knowing the hypotenuse (c), we can find the length of the legs (a and b). Since it's an isosceles triangle, a = b.

Let's call each leg of the triangle 'x'. According to the theorem, this would mean:

x² + x² = 58²,

which simplifies to

2x² = 58².

So,

x² = (58²) / 2,

x = 58 / √2,

x = 58√2 / 2,

x = 29√2 inches.

Finally, the perimeter (P) of the triangle is the sum of the lengths of its sides:

P = hypotenuse + leg + leg = 58 + 29√2 + 29√2 inches = 58 + 58√2 inches.

Therefore, the correct answer is C) 58 + 58√2 inches.