SOLUTION: If the perimeter of a rectangle is 14 inches and its diagonal is 5 inches what is the length and width of the rectangle? I have tried lots of things. I know that the Perimeter =

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Question 337933: If the perimeter of a rectangle is 14 inches and its diagonal is 5 inches what is the length and width of the rectangle?
I have tried lots of things. I know that the Perimeter = 2L + 2W and the Diagonal is the square root of the width squared + the height squared. Other than this i have no clue where to turn. Please help :)

Answer by katealdridge(100)   (Show Source): You can put this solution on YOUR website!
This requires you to write a system of equations
First: therefore,
Second:
In first equation, solve for one of the variables.
Then substitute 7-L for W in second equation.

FOIL
Simplify
set quadratic equation equal to 0.
simplify quadratic by dividing all terms by 2.
Factor-find two numbers that multiply to 12 and add to 7.

Substitute 3 and 4 into W=7-L to find W.
L=3, W=4 or L=4, W=3

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