# A rectangle piece of cardboard is twice as long as it is wide. A 4-cm square is cut out of each corner , and the sides are  turned up to make a box is 616 cm3. find the original dimensions of the card board.

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A rectangle piece of cardboard is twice as long as it is wide. A 4-cm square is cut out of each corner , and the sides are  turned up to make a box is 616 cm3. find the original dimensions of the card board.

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Step 1

Consider x be the width of the rectangle. So, 2x is the length of the rectangle.

Corner cut: A 4 cm square

Volume of the final box is 616 cm3.

Step 2

Now removing 4 cm squares will reduced the length 2x and width each by 8 units.

So, the finial length is (2x – 8) cm and finial width is (x – 8) cm

Also, the height of the box is 4 cm

Therefore, the volume of the box is given by

Step 3

Substituting the volume = 616 an...

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MathAlgebra