Given a right triangle with legs of lengths $20$ and $21$, what is the length of the hypotenuse?

• A. $29$
• B. $28$
• C. $\sqrt{{20}^2+{21}^2}$
• D. $29$

Answer: (D)

Verified step by step guidance

1. Identify that the triangle is a right triangle with legs of lengths 20 and 21, and we need to find the hypotenuse.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse length \(c\) is equal to the sum of the squares of the legs: \(c^2 = a^2 + b^2\).
3. Substitute the given leg lengths into the formula: \(c^2 = 20^2 + 21^2\).
4. Calculate the squares of the legs: \$20^2 = 400\( and \)21^2 = 441\(, so \)c^2 = 400 + 441$.
5. Add the values to get \(c^2 = 841\), then take the square root of both sides to find \(c = \sqrt{841}\), which gives the length of the hypotenuse.