A fence to a rectangular enclosure has a width w, which Is (5m) shorter than its length.
(A).write down an expression for the perimeter of the enclosure.
(B).if the perimeter is not to exceed (150m), find the maximum possible width of the enclosure.
width ---- w
length ---- w+5
P = 2w + 2(w+5)
= 2w + 2w + 10
= 4w + 10
4w + 10 ≤ 150
4w ≤ 140
w ≤ 35
max width is 35 m
To find the expression for the perimeter of the enclosure, let's first define the length.
Given that the width, w, is 5 meters shorter than the length, we can represent the length as (w + 5).
Now, the perimeter of a rectangle is calculated by adding up the lengths of all its sides. In this case, the perimeter will be equal to twice the sum of the length and the width.
(A). Expression for the perimeter:
Perimeter = 2 * (Length + Width)
Substituting the given values, we have:
Perimeter = 2 * ((w + 5) + w)
Perimeter = 2 * (2w + 5)
Perimeter = 4w + 10
(B). To find the maximum possible width of the enclosure when the perimeter does not exceed 150m, we can set up an inequality:
Perimeter ≤ 150
Substituting the expression for the perimeter from part (A), we have:
4w + 10 ≤ 150
Solving this inequality, we can isolate the variable 'w':
4w ≤ 150 - 10
4w ≤ 140
w ≤ 140/4
w ≤ 35
Therefore, the maximum possible width of the enclosure is 35 meters.