Answer :
The length of the rectangular field is 164 yards and the width is 41 yards
From the question,
We are to determine the fields dimensions
From the given information
A rectangular field is four times as long as it is wide
That is
l = 4w -------- (1)
The perimeter of a rectangle is given by
P = 2(l + w)
Where
P is the perimeter
l is the length
and w is the width
From the given information
The perimeter of the field is 410 yards
∴ 2(l + w) = 410 ------ (2)
Substitute equation (1) into equation (2)
2(4w + w) = 410
2(5w) = 410
10w = 410
∴ w = 410 ÷ 10
w = 41 yards
Substitute the value of w into equation (1)
l = 4(41)
l = 164 yards
Hence, the length of the rectangular field is 164 yards and the width is 41 yards.
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