Answer:

Sure, let's solve this problem. We have a rectangular backyard with an area of 16 square meters and a perimeter of 18 meters.

Let's assume the length of the rectangle is L meters, and the width is W meters.

The formula for the area of a rectangle is:

Area = Length x Width

So, we have:

16 = L x W

The formula for the perimeter of a rectangle is:

Perimeter = 2(Length + Width)

Given that the perimeter is 18 meters, we can write:

18 = 2(L + W)

Now, we have a system of two equations:

1. 16 = L x W

2. 18 = 2(L + W)

We can solve this system of equations simultaneously to find the dimensions of the rectangular backyard.

First, let's solve equation (2) for L + W:

18 = 2(L + W)

L + W = 18/2

L + W = 9

Now, we can use this result to find L and W in equation (1):

16 = L x W

We need two numbers that multiply to 16 and add up to 9. Those numbers are 4 and 4. So, we can write:

L = 4 meters

W = 4 meters

So, the dimensions of the rectangular backyard are:

Length (L) = 4 meters

Width (W) = 4 meters

This means it's a square backyard with sides of 4 meters each.