Question

Two gardens are being fenced in. Both gardens will require the same amount of fencing​ (both gardens have the same perimeter in​ meters). One garden is in the shape of a square and the other is in the shape of an equilateral triangle. Each side of the triangle is 1 meters longer than each side of the square.

Answer 1

The side length of the square is 3 meters.

The side length of the triangle is 4 meters.

Explanation:

This is basically a systems of equations word problem.

To solve this, we have to create two different equations. Let's assume
`s` is the side length of the square and
`t` is the side length of the triangle.

We can make the equation
`4s=3t`, since the perimeters are the same. (A square has 4 sides, a triangle has 3 - multiplying by the side length of each will get perimeter)

We also know that the side length of the triangle is 1 meter longer than the side length of the square, so the equation here becomes
`t = s+1`.

Now, let's substitute the second equation (
`t = s+1`) into the first (
`4s=3t`).

`4s = 3(s+1)`

Apply the distributive property:

`4s = 3s+3`

Subtract 3s from both sides:

`s=3`

So the side length of the square is 3. We can now plug it into the equation
`t = s + 1` to find the side length of the triangle.

`t = 3+1\\\\t=4`

Hope this helped!