A garden 7 m by 12 m will be expanded by planting a border of flowers. The border will be of the same width around the entire garden and has an area of 92m2 _____ Algebraic expression.
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Step-by-step explanation:
A1 = area of garden including the border (w) = (7+w)*(12+w)
A2 = area of garden = 7 * 12 = 84
Area of border = (7+w)*(12+w) - 84 = 92
(7+w)*(12+w) = 176
w^2 + 19w + 84 = 176
this is a quadratic equation
w^2 + 19w -92 = 0
factor this equation
(w-4) * (w+23) = 0
w is 4 or -23
our answer has to be w > 0, so w = 4 m
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