The length of the hypotenuse of an isosceles right triangle...

The length of the hypotenuse of an isosceles right triangle is 24 inches. What is the length of one leg of the triangle, rounded to the nearest tenth of an inch?
A) 13.9 inches
B) 17.0 inches
C) 33.9 inches
D) 41.6 inches

Key Concepts

Rounding

Rounding is the process of adjusting a numerical value to a specified degree of precision. In problems involving measurements, such as finding a triangle's side length, rounding is used to report the final answer in a clear and practical manner, such as to the nearest tenth.

Square Roots

Taking the square root of both sides of an equation is a common technique to solve for a variable squared. In the context of triangles, this operation is essential after applying the Pythagorean Theorem to find the actual length of the leg.

Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse. For an isosceles right triangle, this theorem simplifies to an equation where twice the square of one leg equals the square of the hypotenuse, which is instrumental in finding the leg lengths.

Isosceles Right Triangle

An isosceles right triangle is a triangle with a right angle and two sides of equal length. This unique geometry means that the two legs are congruent and that the hypotenuse is related to the legs by a constant factor, making it easier to solve for unknown side lengths.

Algebraic Manipulation

Algebraic manipulation involves rearranging equations, such as isolating the variable representing the leg of the triangle. When applied to the equation derived from the Pythagorean Theorem for an isosceles right triangle, this manipulation helps in expressing the leg in terms of the hypotenuse.

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