Question

the hypotenuse of a triangle is one foot more than twice the length of the shorter legal. the longer leg is seven feet longer than the shorter leg. find the dimensions of the triangle

Answer 1

8, 15, 17

You can do this by using the Pythagorean Theorem and setting the sides equal to

shorter leg = x
longer leg = x + 7
hypotenuse = 2x + 1

Then solve so that one side is equal to zero and use the quadratic formula.

Answer 2

The dimensions of the right triangle are 8, 15 and 17.

Explanation:

First, we need to express the problem in equations. We will use the pythagorean theorem because we have a right triangle.

The longer side we're gonna call it
`l`.

The shorter side will be
`s`

The hypothenuse will be
`h`

Now, the problem is giving us relations.

"The hypothenuse is one foot more than twice the length of the shorter leg"

This can be expressed like
`h=1+2s`

"The longer leg is seven feet longer than the shorter leg"

This can be expressed like
`l=7+s`

Now, applying the pythagorean theorem, we have:

`h^(2)=s^(2)+l^(2)\\(1+2s)^(2)= s^(2)+(7+s)^(2)\\1+4s+4s^(2)= s^(2)+49+14s+s^(2)\\ 2s^(2)-10s-48=0\\s^(2)-5s-24=0\\(s-8)(s+3)=0\\s=8\\s=-3`

From these values, we use the positive one, because it refers to length. Replacing this value in each expression, we find each element of the triangle:

`h=1+2s=1+2(8)=17`

`l=7+s=15`

Therefore, the dimensions of the right triangle are 8, 15 and 17.