The height of a rectangular solid is five times its widthand its length is 8 times its height. if volume is 102.4cm^2find length

32cm

Step-by-step explanation:

From the question, we can deduce that

1. Height= 5(width)

2. Length=8(height)

which is also 8(5(width))=40(width)

The volume is length x width x height =102.4cm3

Now, we’ll put the volume equation in terms of width alone, as we’ve deduced above

40(width) x 5(width) x width = 102.4

(Solve the equation)

200(width)^3=102.4

(Divide both sides by 200)

(width)^3=102.4/200

(width)^3=512/1000

(Take cube root of both sides)

Width=8/10 or 0.8

Hence, the length=40(width)

Length=40 x 0.8

=32

Therefore, the length is 32cm

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