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Mike wants to redesign a box. Currently, it’s length is 20 cm, it’s width is 30 cm and it’s height is 40cm. he wants to keep the volume and the length unchanged and increase the height by 25 percent. What will be the new width of the box?

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sqdancefan

Answer:

  24 cm

Step-by-step explanation:

The product of height and width will remain the same, so the new width (w) will be given by ...

  w·(new height) = (old width)·(old height)

  w·(1.25·40 cm) = (30 cm)(40 cm)

  w = (30 cm)/1.25 = 24 cm . . . . . . . divide by 1.25·40 cm and simplify

_____

This derives from the fact that volume and length are unchanged. The formula for the volume in terms of length, width, and height is ...

  V = LWH

Then the product of W and H is the constant ...

  V/L = WH . . . . . divide by L

For our purpose, we only need to know that V and L are unchanged, so the product WH is unchanged. We don't need to know their values.

Of course, increasing the height by 25% is equivalent to multiplying it by 1.25:

  H + 25/100·H = H·(1 + 0.25) = 1.25H

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