SOLUTION: A rectangular parcel of land is 70 feet longer than it is wide. Each diagonal is 130 feet long. What are the dimensions of the parcel? I know you have to use the pythagorean the

Question 183395: A rectangular parcel of land is 70 feet longer than it is wide. Each diagonal is 130 feet long. What are the dimensions of the parcel?
I know you have to use the pythagorean theorem but I have no clue what to do. Please help! :)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let L=length and W=width

Since the "land is 70 feet longer than it is wide", this tells us that (ie take the width and add 70 to get the length)

If you cut the rectangle in half along the diagonal, you'll find that the resulting pieces will be right triangles. So we can use Pythagorean's Theorem to find the legs (since we're given the hypotenuse)

Start with Pythagorean's Theorem

Plug in , and (this is the given diagonal)

Square 130 to get 16900

Plug in

FOIL

Subtract 16900 from both sides.

Combine like terms.

Notice how the equation is now in the form where , , and

Plug in , , and

Square 140 to get 19600

Multiply to get 96000

Combine like terms in the radicand (everything under the square root)

Simplify the square root

Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one possible answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another possible answer is

However, it doesn't make sense to have a negative width. So we must ignore this possible solution

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So this means that the only answer is and that the width is 50 feet.

Go back to the first equation

Plug in

Add

So the other answer is which means that the length is 120 feet.

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Answer:

So the length is 120 feet and the width is 50 feet.
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