ACT Math · Triangles and similarity

In a 45-45-90 triangle, each leg has length 8. Which value is closest to the length of the hypotenuse?

In a 45-45-90 triangle, each leg has length 8. Which value is closest to the length of the hypotenuse?

Answer and explanation

Answer: G: 11.3

In a 4545-4545-9090 triangle, the hypotenuse is the leg times 2\sqrt2. So the hypotenuse is 82≈8(1.414)≈11.38\sqrt2\approx8(1.414)\approx11.3, choice G. Check with the Pythagorean theorem: 82+82=128≈11.3\sqrt{8^2+8^2}=\sqrt{128}\approx11.3. Choice J (1616) doubles the leg, which would be the sum of the legs. Choice F (88) is the length of a leg; the hypotenuse must be longer. Choice H (13.913.9) is 838\sqrt3, the multiplier from a 3030-6060-9090 triangle. Match the ratio to the triangle type.

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