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):
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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