Question

The area of a rectangle is 440 square inches. The length of the rectangle is 29 inches more than its width. What is the length of the rectangle?

Answer 1

The length of regtangle is 40 inches

Answer 2

the length of the rectangle is either -11 inches or 40 inches.

• Let the length of the rectangle be L.

• Let the width of the rectangle be W.

Given the following data;

• Area of rectangle = 440 square inches

Translating the word problem into an algebraic equation, we have;

$L = W + 29$

To find the length of the rectangle;

Mathematically, the area of a rectangle is given by the formula;

$Area = L * W$

Substituting the values into the formula, we have;

$440 = (W + 29) * W\\\\440 = W^{2} + 29W$

Rearranging the equation, we have;

$W^{2} + 29W - 440 = 0$

W e would solve the quadratic equation by factorization;

$W^{2} + 40W - 11W - 440 = 0\\\\W(W + 40) - 11(W + 40)\\\\(W + 40)(W- 11)$

Width, W = -40 0r 11 inches.

Next, we would find the length of the rectangle;

When Width, W = -40;

$L = W + 29$

$L = -40 + 29$

Length, L = -11 inches

When Width, W = 11;

$L = W + 29$

$L = 11 + 29$

Length, L = 40 inches

Therefore, the length of the rectangle is either -11 inches or 40 inches.

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