In the right triangle shown, one leg measures $21$ units and the other leg measures $28$ units. What is the length of the hypotenuse $x$?

• A. $x=37$
• B. $x=28$
• C. $x=21$
• D. $x=35$

Answer: (D)

Verified step by step guidance

1. Identify the given sides of the right triangle: the two legs are 21 units and 28 units.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (x) is equal to the sum of the squares of the legs: \(x^2 = a^2 + b^2\).
3. Substitute the given leg lengths into the formula: \(x^2 = 21^2 + 28^2\).
4. Calculate the squares of the legs separately: \$21^2 = 441\( and \)28^2 = 784$.
5. Add these values to find \(x^2\): \(x^2 = 441 + 784\), then take the square root of both sides to solve for \(x\): \(x = \sqrt{441 + 784}\).