Problem:
A rectangular field is half as wide as it is long and is completely enclosed by x yards of fencing. The area in terms of x is:
Answer Choices:
A. 2x2
B. 2x2
C. 92x2
D. 18x2
E. 72x2
Solution:
Let the dimensions of the rectangular field be a width of w and a length of 2w. The variable x represents the perimeter of the field.
P=2(w+2w)=6w=x
From this relationship, we can express the width and length in terms of x:
Width: w=6xandLength: 2w=3x
Now, we can find the area, A, by multiplying the width and length.
A=(width)⋅(length)=(6x)⋅(3x)=18x2
Therefore, the area of the field in terms of x is 18x2.