Question

Can you find a cuboid (with edges of whole number lengths) that has a surface area of exactly 100 square units?

Answer 1

`x = 2` ;
`y = 4` and
`z = 7`

Explanation:

Given

Let the sides of the cuboid be: x, y and z

`Surface\ Area = 100`

Required

Find x, y and z

The surface area is calculated as:

`Surface\ Area = 2*(xy + xz + yz)`

Substitute
`Surface\ Area = 100`

`100 = 2*(xy + xz + yz)`

Divide both sides by 2

`50 = xy + xz + yz`

Rewrite as:

`xy + xz + yz =50`

Now, we use trial by error method to determine the values of x, y and z.

Let
`x = 2` and
`y = 4`

Solve for z:

`2 * 4 + 2*z + 4*z =50`

`8 + 2z + 4z =50`

Collect like terms

`2z + 4z =50-8`

`6z =42`

Divide both sides by 6

`z = (42)/(6)`

`z = 7`

So, we have:

`x = 2` ;
`y = 4` and
`z = 7`

The above values are all integers;

Hence, it is possible to determine a cuboid with the stated requirement