A farmer wants to build a new pen for his chickens. He wants the chickens to have as much freedom and room as possible. The fencing panels come in 1-meter panels. The farmer can vary the lengths of the sides of the pen, which will affect the area. Planning restrictions say that the pen must be rectangular the length of all four sides must add up to 100m.

Question

A farmer wants to build a new pen for his chickens. He wants the chickens to have as much freedom and room as possible. The fencing panels come in 1-meter panels. The farmer can vary the lengths of the sides of the pen, which will affect the area. Planning restrictions say that the pen must be rectangular the length of all four sides must add up to 100m.

If x represents the width of the rectangle write down in terms of x an algebraic expression for the length.

Answer 1

Assuming the pen is rectangular,

let the width be x
You know the 2 widths + 2 lengths = 100
width + length = 50
x + length = 50
length = 50-x

Answer 2

To write down the length of the rectangle in terms of x, we need to understand the relationship between the width and length of the rectangle.

Since the length of all four sides of the rectangular pen must add up to 100m, we can express this relationship using variables.

Let's assume:
x = width of the rectangle (in meters)
L = length of the rectangle (in meters)

According to the defined restrictions, we know that the width (x) and length (L) of the rectangle have a sum of 100m.

So, the equation representing this relationship is:
2x + 2L = 100

Now, let's rearrange the equation to isolate the length (L) in terms of x:
2L = 100 - 2x
Dividing both sides of the equation by 2, we have:
L = 50 - x

Therefore, the algebraic expression for the length of the rectangle in terms of x is:
L = 50 - x