Area = Length*Width
Information you are given:
Area = 105cm^2
Length = width + 8
105 = (width + 8)*width
105 = width^2 + 8*width
105 = w^2 + 8w
rearranging we get a quadratic:
w^2 + 8w - 105 = 0
w^2 - 7w +15w - 105 = 0
w(w - 7) + 15(w - 7) = 0
(w - 7)(w + 15) = 0
The two possible solutions are
width = 7 or width = -15
Well, the width must be a positive measurement so we take the width = 7
So the answer is:
Width = 7
Length = 7 + 8 = 15
Hope that helps
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