Answer:
Volume = 7WH - (1/2)W^2H
Step-by-step explanation:
The base consists of the length (L) and the width (W). It is rectangular, so the perimeter would be the sum of all four sides:
Perimeter = L + W + L +W,
or Perimeter = 2L + 2W
We are told that 2L + 2W = 28cm [The perimeter is 28 cm]
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The volume of the box is given by:
Volume = L*W*H [Length x Width x Height]
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Let's rearrange the first equation and use it in the second:
2L + 2W = 28cm
2L = 28cm - 2W
L = (28cm - 2W)/2
L = (14 - W)
Now use this definition of L (14 - W) in the second equation:
Volume = L*W*H
Volume = (14 - W)/2)*W*H
Volume = (7-(1/2)W)*W*H
Volume = 7WH - (1/2)W^2H
This can also be written as: Volume = WH(7 - (1/2)W)
