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What are the dimensions of a rectangle with length 5 in longer than its width which has 1 inside squares cut from the corners and the flaps folded up to form an open box of volume 500 cu in?
Wiki User
∙ 7y ago
It is 22 in by 27 in.
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How it is solved:
The rectangle is 5 in longer than its width, so the dimensions can be given in terms of its width:
Its dimensions are width by (width+5)
In removing 1 inch squares from the corners, he flaps are going to be (width-2) and (width+5-2) = (width-3) long.
Thus the box formed will have volume:
volume = (width - 2) in × (width + 3) in × 1 in
→ volume = width² + width - 6 in³
But we are told this is 500 in³; thus:
width² + width - 6 in³ = 500 in³
→ width ² + width - 506 = 0
→ (width + 23)(width - 22) = 0
→ width = -23 or 22
As a length cannot be negative, the width must be 22 in
which means the original rectangle is 22 in by 22+5 in = 27 in
Wiki User
∙ 7y ago
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