Help me Please
World Problems
Find the length and width.
The perimeter of a floor is 40 feet and its area 96 square feet.
Perimeter =2[L + W]
Area =L x W
2[L + W] = 40
L x W =96, solve for L, W
L=12 and W = 8 - feet, or:
W = 12 and L = 8 - feet.
Remember, Manuel.....
Perimeter = 2W + 2L and Area = LW
So
40 = 2W + 2L divide through by 2
20 = W + L subtract W from both sides
20 - W = L (1)
And
96 = LW sub in (1) for L.....and we have
96 = (20 - W) * W simplify
96 = 20W - W^2 add W^2 to both sides, subtract 20W from both sides
W^2 - 20W + 96 = 0 factor.....-8 and - 12 are what we need
(W - 8) ( W - 12) = 0
Set each factor to 0 and solve for W
W = 8 or W = 12
So, Manuel....we can let W = 8....so
L = 20 - 8 = 12
So....Width = 8 and Length = 12
Check - perimeter = 2W + 2L = 2(8) + 2(12) = 16 + 24 = 40
area = 8 * !2 = 96
Hope that helped......!!!!