Deon has 26 meters of wire fencing to make a rectangular pen for his two show lambs. He has learned that each lamb should have 20m^2 of space. Does he have enough fencing for an area of 40m^2? Use a table to determine your answer.

To determine if Deon has enough wire fencing to make a rectangular pen with an area of 40m² (20m² for each of the two lambs), we need to consider the properties of rectangles and how perimeter relates to area.

The area (A) of a rectangle is given by the formula A = length × width.

Deon needs a total area (A) of 40m² for both lambs.

In a rectangle, the perimeter (P) is the total distance around the outside of the shape and is calculated by adding together twice the length and twice the width: P = 2 × length + 2 × width.

Deon has a total of 26 meters of fencing.

Let's define: length = l meters width = w meters

Deon wants: Area (A) = l × w = 40m² Perimeter (P) = 2l + 2w = 26m

Since Deon needs an area of 40m², let's see what combinations of length and width can give us this area and check if any combination has a perimeter of 26m or less.

Table: Length (m) | Width (m) | Area (m²) | Perimeter (m) 1 | 40 | 40 | 82 2 | 20 | 40 | 44 4 | 10 | 40 | 28 5 | 8 | 40 | 26 8 | 5 | 40 | 26 10 | 4 | 40 | 28 20 | 2 | 40 | 44 40 | 1 | 40 | 82

From the table, we can see that when the length is 5 meters and the width is 8 meters, or when the length is 8 meters and the width is 5 meters, the perimeter is 26 meters, which matches exactly the amount of fencing Deon has.

So yes, Deon has exactly enough fencing to create a rectangular pen with an area of 40m² for his two show lambs.