Answer: W = 29 and L = 16
Explanation:
Perimeter, P, of a rectangle is 2L+2W (L and W are length and width)
Area, A, of a rectangle is L*W
We know:
P = 90 meters
A = 464 meters^2
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90 meters = 2L+2W
464 meters^2 = L*W
Rearrange the second equation:
L = (464 meters^2)/W
Use this value of L in the first equation:
90 meters = 2L+2W
90 meters = 2*((464 meters^2)/W)+2W
90 meters = ((928 meters^2)/W)+2W
90 meters = ((928 meters^2)/W)+2W
90*W meters = (928 meters^2)+2W^2 Multiply both sides by W
2W^2 -90W + 928 m^2 = 0
W^2 -45W + 464 m^2 = 0 [Divide both sides by 2]
Use the quadratic equation or factor the expression:
(x-16) and (x-29) , The solutions are 29 and 16, each in meters.
[(x-16)*(x-29)= x^2 -45x + 464
W = 29 and L = 16
P = 2*(29)+2(16) This is equal to 90 meters Checks.
A = 29*16 = 464 m^2 Checks