SOLUTION: The perimeter of a rectangular concrete slab is 82 feet and its area is 418 square feet. What is the length of the longer side of the slab? I started by making two seperate equa

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Question 308574: The perimeter of a rectangular concrete slab is 82 feet and its area is 418 square feet. What is the length of the longer side of the slab?
I started by making two seperate equations, one for perimeter and one for area. I came up with 2L+2W=82 and L*W=418. I don't know where to go from here.

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify the first equation by dividing both sides by 2.
L+W= 41

Solve for W:
W=41-L

Substitute back into the other equation:
LW=418
L(41-L)=418
41L-L^2-418=0

Multiply both sides by -1:
L^2 -41L +418=0

The hard part is to find two numbers that multiply to give you 418, and that adds up to 41. The way I teach this is to start with 1 and make a list as follows:

1*418
2*209
11*38
19*22

This is the combination!
(L-19)(L-22)=0
L=19 or L=22

This means that 19 is the width and 22 is the length.

Dr. Robert J. Rapalje, Retired

P.S. Nice problem!!!