The total length of the fence is 450 ft. This means that the perimeter of the fence is 450 ft.
Given that the width, w is 10 feet less than half the length, l, it means that the fence is rectangular. We would apply the formula for determining the perimeter of a rectangle which is expressed as
Perimeter = 2(length + width)
From the information given,
w = l/2 - 10
w = 0.5l - 10
Therefore, the equation that could be used to determine the dimensions of his yard is
2(0.5l - 10 + l) = 450
Let us replace x with l. it becomes
2(0.5x - 10 + x) = 450
x - 20 + 2x = 450
2x + x - 20 = 450
We would factor out 2 from x - 20
2x + 2(0.5x - 10) = 450
The first option is the correct answer
