The short leg of a right triangle is 5 feet long. The long leg of the triangle is 10 feet long. According to the Pythagorean Theorem, which of the following is the length of the hypotenuse?

Sure, let's solve this step by step using the Pythagorean Theorem.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this is expressed as:

$c^2 = a^2 + b^2$

Given:

• The short leg (a) is 5 feet.
• The long leg (b) is 10 feet.

We need to find the length of the hypotenuse (c).

Step 1: Square the lengths of the short leg and the long leg. $a^2 = 5^2 = 25$ $b^2 = 10^2 = 100$

Step 2: Add the squares of the short leg and the long leg. $a^2 + b^2 = 25 + 100 = 125$

Step 3: Take the square root of the sum to find the length of the hypotenuse. $c = \sqrt{125}$

Step 4: Simplify the square root if possible. $\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5}$

Therefore, the length of the hypotenuse is $5\sqrt{5}$ feet.