the length of the rectangle is either -11 inches or 40 inches.
Given the following data;
Translating the word problem into an algebraic equation, we have;
[tex]L = W + 29[/tex]
To find the length of the rectangle;
Mathematically, the area of a rectangle is given by the formula;
[tex]Area = L * W[/tex]
Substituting the values into the formula, we have;
[tex]440 = (W + 29) * W\\\\440 = W^{2} + 29W[/tex]
Rearranging the equation, we have;
[tex]W^{2} + 29W - 440 = 0[/tex]
W e would solve the quadratic equation by factorization;
[tex]W^{2} + 40W - 11W - 440 = 0\\\\W(W + 40) - 11(W + 40)\\\\(W + 40)(W- 11)[/tex]
Width, W = -40 0r 11 inches.
Next, we would find the length of the rectangle;
When Width, W = -40;
[tex]L = W + 29[/tex]
[tex]L = -40 + 29[/tex]
Length, L = -11 inches
When Width, W = 11;
[tex]L = W + 29[/tex]
[tex]L = 11 + 29[/tex]
Length, L = 40 inches
Therefore, the length of the rectangle is either -11 inches or 40 inches.
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