A = L × W = 450 m^2 L = W+7 So: 450m^2 = (W+7)(W) 450m^2 = W^2 + 7W W^2 + 7W -450 = 0 Now to factor the quadratic we need to think of what factors of 450 have a difference of 7?? Well 15×30= 450, but there difference is 15. So let's try two more... 25×18= 450. Is 25-18 = 7? YES!! So we know the factors are: (W-18)(W+25) = 0 So W-18 = 0, W = 18m And W+25 = 0, W = -25m We can't have a negative length in real life, so the only true solution is W = 18m Do the shorter side (W) is 18m long And the longer side (L) = W + 7 = 25 So the perimeter (P) = 2 (L+W) = 2 (25+18) P = 2 (43) = 86m
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