SOLUTION: what is the length and width of a rectangle if the perimeter is 24m and the area is 35m2?

Question 288390: what is the length and width of a rectangle if the perimeter is 24m and the area is 35m2?
Answer by jaydducote(11) (Show Source): You can put this solution on YOUR website!
Area=length times width, or A=LW
Perimeter=2W+2L
We know the perimeter is 24m, so 24=2W+2L
We know the area is 35 square meters, so 35=LW
Now you need to do substitution to solve. You have to solve for either L or W in terms of the other variable. I would solve the first one for W:
24=2W+2L
subtract 2L from both sides
24-2L=2W
now divide both sides by 2
12-L=W
so we know that W=12-L. Substitute that into the other equation:
35=LW
35=L(12-L)
distribute the L
35=12L-L^2
This now looks tricky, there is a square term, so we will need to factor
Move everything to the left side
L^2-12L+35=0
Now, think about which two numbers add to twelve and multiply to get 35. Think of the factors of 35. Only 7 times 5 works, which happen to add to 12!
Since we have a -12L but a +35, and we know we are adding to get to 12, not subtracting, we should conclude that both the 7 and 5 must be negative. Factored, we get this:
(L-5)(L-7)=0
This means that our two "zeros" or solutions are the numbers that make this statement true. If L is 5 or 7, the entire value is 0, so those are our answers. W=5, L=7.
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