Advanced MathVery hardSize of the corner squares cut to make a box base
Advanced Math practice question
Equal squares are cut from the four corners of a rectangular sheet of card measuring 20 centimetres by 30 centimetres, and the sides are folded up to form an open box whose base has an area of 336 square centimetres. What is the side length, in centimetres, of each square that was cut out?
Answer: 3
(20 − 2s)(30 − 2s) = 336 → 4s² − 100s + 600 = 336 → s² − 25s + 66 = 0 → (s − 3)(s − 22) = 0. Since 2s < 20, s = 3.
Common wrong answers
- If you answered 6
- 6 is 2s, the total removed from each side.
- If you answered 14
- 14 is the width of the base (20 − 6), not the square's side.
- If you answered 22
- 22 is the other root, but it would exceed the sheet's width.
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