PLEASE HELP ASAP ?

The hypotenuse of a right triangle is 5 ft long. The shorter leg is 1 ft shorter than the longer leg. Find the side lengths of the triangle.
Length of the shorter leg:
Length of the longer leg: Length of the hypotenuse:

this doesn’t help at all nor do i understand but ok.

You need to review the Pythagorean Theorem. In a right triangle, with legs a and b, and hypotenuse c

a^2 + b^2 = c^2

To find the side lengths of the triangle, let's assign variables to the unknown lengths.

Let's say the length of the longer leg is "x" ft.

According to the problem, the shorter leg is 1 ft shorter than the longer leg. So, the length of the shorter leg would be "x - 1" ft.

Since the hypotenuse of a right triangle is given as 5 ft, we can use the Pythagorean theorem to solve for the side lengths.

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

Using this theorem, we can set up the following equation:

(x - 1)^2 + x^2 = 5^2

Simplifying the equation:

x^2 - 2x + 1 + x^2 = 25

Combining like terms:

2x^2 - 2x + 1 = 25

Subtracting 25 from both sides:

2x^2 - 2x - 24 = 0

Dividing both sides by 2:

x^2 - x - 12 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula.

Factoring the equation:

(x + 3)(x - 4) = 0

This gives two possible solutions for x: x = -3 or x = 4. However, since we are dealing with lengths, the value of x cannot be negative. So, x = 4 ft.

Therefore, the length of the shorter leg would be x - 1 = 4 - 1 = 3 ft.
The length of the longer leg would be x = 4 ft.
The length of the hypotenuse is given as 5 ft.

So, the side lengths of the triangle are:
Length of the shorter leg: 3 ft
Length of the longer leg: 4 ft
Length of the hypotenuse: 5 ft

does 3-4-5 look familiar?

You can save yourself some calculation by learning a few of the basic Pythagorean triples, such as
3-4-5, 5-12-13, 8-15-17, 7-24-25
and their multiples.

Of course, you can solve it algebraically via
x^2 + (x+1)^2 = 5^2