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23 February, 15:11

The length of a rectangle is 8 feet more than the width. If the width is increased by 4 feet, and the length is decreased by 5 feet, the area remains the same. Find the dimensions of the original rectangle.

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  1. 23 February, 15:30
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    Width = 12 feet

    Length = 20 feet

    Step-by-step explanation:

    The area of a rectangle is A = l*w. Here the length is 8 feet more than the width or 8 + w and the width is w. So the area is A = w (8+w) = 8w + w²

    If the dimensions are changed then the expressions will change. The width is increased by 4 feet. This means the width w becomes w + 4. The length is decreased by 5 feet. This means the length becomes 8 + w - 5 = 3 + w. So the area of the new triangle is A = (w+4) (3+w) = w² + 7w + 12.

    Since the areas are the same, set them equal to each other and solve for w.

    w² + 7w + 12 = 8w + w² Subtract w² from both sides.

    7w + 12 = 8w Subtract 7w from both sides.

    12 = w

    The original width w is 12 feet. This means the original length which was 8 + w = 8 + 12 = 20 feet.
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