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 =

Algebra ->  Rectangles -> 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 =      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
This requires you to write a system of equations
First: 2L%2B2W=14 therefore, L%2BW=7
Second: L%5E2%2BW%5E2=5%5E2
In first equation, solve for one of the variables. W=7-L
Then substitute 7-L for W in second equation.
L%5E2%2B%287-L%29%5E2=5%5E2
L%5E2%2B49-14x%2BL%5E2=25 FOIL %287-L%29%5E2
2L%5E2-14x%2B49=25 Simplify
2L%5E2-14x%2B24=0 set quadratic equation equal to 0.
L%5E2-7x%2B12=0 simplify quadratic by dividing all terms by 2.
%28L-3%29%28L-4%29=0 Factor-find two numbers that multiply to 12 and add to 7.
L=3+or+L=4
Substitute 3 and 4 into W=7-L to find W.
L=3, W=4 or L=4, W=3