Question 1036138
The area of a rectangle is {{{A = L*W}}} where A is the area, L is the length and W is the width.



In this case, A = 143, L = x+7 and W = x+9. 



Let's plug these expressions in. Then let's solve for x.



{{{A = L*W}}}



{{{A = (x+7)*(x+9)}}}



{{{143 = (x+7)*(x+9)}}}



{{{143 = x*(x+9)+7*(x+9)}}}



{{{143 = x^2+9x+7x+63}}}



{{{143 = x^2+16x+63}}}



{{{143-143 = x^2+16x+63-143}}}



{{{x^2+16x-80=0}}}



{{{(x-4)(x+20)=0}}}



{{{x-4=0}}} or {{{x+20=0}}}



{{{x=4}}} or {{{x=-20}}}



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The possible solutions are {{{x=4}}} or {{{x=-20}}}



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If {{{x=4}}}, then



L = x+7 = 4+7 = 11



W = x+9 = 4+9 = 13



So if x = 4, then the rectangle is 13 meters by 11 meters. Notice how 11*13 = 143



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If {{{x = -20}}}, then



L = x+7 = -20+7 = -13



W = x+9 = -20+9 = -11



but having negative side lengths doesn't make much sense. So we ignore the solution x = -20



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The only practical solution is x = 4



That leads to the dimensions of the rectangle being 13 meters by 11 meters