Question

A rectangle has length `3sqrt5 - 4sqrt3` feet and width `2sqrt5 + 5sqrt3` feet, what is the perimeter?

Answer 1

The perimeter of the rectangle is undefined.

But if it did exist, it would be `10sqrt5 + 2 sqrt3`.

Explanation:

The formula for perimeter is `P = 2l + 2w`

The width `w` is `2sqrt5+5sqrt3`
The length `l` is `3sqrt5 - 4 sqrt3`

Hmm... the length is less than 0 (it is `-0.22`). Are you sure that's what the problem says? If the problem is correct, then the rectangle can't exist, so its perimeter is undefined. You can't have a negative length!

Let's go ahead and pretend we could have negative sides.
In that case, the perimeter is:

`P = 2(3sqrt5-4sqrt3)+2(2sqrt5+5sqrt3)`

`P = 6sqrt5-8sqrt3+4sqrt5+10sqrt3`

`P = 10sqrt5 + 2 sqrt3`

Final Answer