Suppose you want to construct a rectangular prism ie a box

. Suppose you want to construct a rectangular prism (i.e. a box enclosed on all sides) with the 30 square feet of cardboard. What are the possible dimensions (length x width x height) of the prism if the dimensions are whole numbers?

Solution

Area of squareboard = 30 sq feet and we have to construct rectangular prism.

It means - Total surface area of rectangular prism is 30 Sq ft.

so, 2(lb+bh+lh)=30

lb+bh+lh = 15

by trying with different combination of number from 1 to 7

we got below 2 combination for satisfying the condition

1. l=7, b=1, h=1

2. l=3, b=3, h = 1

Now, these condition can have different permutation - means you can put the value of h at b and b at h OR

l at b and b at l and so on. But basically these combination will satisfy the given conditon.

Possible dimension = (1*1*7) and (3*3*1)