Do you hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg the longer leg is 7 feet longer than the shorter leg find the dimensions of the triangle

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

Step-by-step explanation:

We are given where is the hypotenuse and is the length of the shorter leg.

We got this equation from reading that the "hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg". I replaced the "hypotenuse of a triangle" with , "is" with , "1 foot more than" with and finally "twice the length of the shorter leg" with .

We also have "longer leg is 7 feet longer than the shorter leg".

I'm going to replace "longer leg" with .

I'm going to replace "is" with .

I'm going to replace "7 feet longer than the shorter leg" with .

So we have the equation .

So we have a right triangle since something there is a side being referred to as the hypotenuse. We can use Pythagorean Theorem to find a relation between all these sides.

So by Pythagorean Theorem, we have: .

Let's make some substitutions from above:

Let's expand the powers using:

Applying this now:

Combine like terms on right hand side:

Subtract everything on left hand side to get 0 on that side:

Simplify:

Reorder into standard form for a quadratic:

Every term is even and therefore divisible by 2. I will divide both sides by 2:

I'm going to see if this is factoroable.

We need to see if we can come up with two numbers that multiply -24 and add up to be -5.

Those numbers are -8 and 3.

So the factored form is:

This implies that either os .

The first equation can be solved by adding 8 on both sides: .

The second equation can be solved by subtracting 3 on both sides: .

The only solution that makes sense for is 8 since it can't the shorter length cannot be a negative number.

So the dimensions of the right triangle are:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

25% is the answer