Answer:
Length = 208 yards
Width = 54 yards
Step-by-step explanation:
Let the length of the field be "x" yards and the width be "y" yards. Its given that the length is 8 less than quadruple(4 times) the width. So x is 8 less than 4y. We can write this in equation as:
x = 4y - 8 Equation 1
Perimeter of the field is given to be 524 yards. Since, the field is rectangular, its perimeter is calculated as:
Perimeter = 2 (Length + Width)
Using the values, we get:
2(x + y) = 524 Equation 2
Substituting the value of x from Equation 1 into Equation 2, we get:
2(4y - 8 + y) = 524
2(5y - 8) = 524
5y - 8 = 524/2
5y - 8 = 262
5y = 262 + 8
5y = 270
y = 54 yards
Substituting the value of y in Equation 1, we get:
x = 4y - 8 = 4(54) - 8 = 208 yards
Thus, the length of the playing field is 208 yards and its width is 54 yards.
