The length of one leg of a right triangle is 8ft. The length of the hypothenuse is 2feet longer than the other leg. Find the length of the hypothenuse and the other leg.

The length of the hypothenuse is _______ ft.
The length of the other leg is ___________ft.

recognize the 3-4-5 triangle scaled up to 6-8-10?

To find the length of the hypotenuse and the other leg in a right triangle, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's use this theorem to solve the problem:

Given:
Length of one leg = 8 ft

We are also given that the length of the hypotenuse is 2 feet longer than the other leg. Let's call the length of the other leg "x", then the length of the hypotenuse is "x + 2".

Now we can apply the Pythagorean theorem:

(8)^2 + (x)^2 = (x + 2)^2

Simplifying the equation:

64 + x^2 = x^2 + 4x + 4

Rearranging the equation to isolate the variable:

0 = 4x - 60

Solving for x:

4x = 60

x = 60 / 4

x = 15

Therefore, the length of the other leg is 15 ft.

To find the length of the hypotenuse:

Length of the hypotenuse = x + 2

Substituting the value of x:

Length of the hypotenuse = 15 + 2 = 17 ft

So, the length of the hypotenuse is 17 ft and the length of the other leg is 15 ft.