Question

A School is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yard longer than its width. Determine algerbraically the dimensions of the soccer field in yards.

Answer 1

Let x by the length and y be the width
Area = x y
x y = 6000

Since the length must be 40 yards longer than the width
x = y + 40

Substituting x to the area

(y +40) y = 6000
y^2 +40y - 6000 = 0

This is quadratic equation. Using the quadratic formula we get the positive value of y,
y = 60
So,
x = y + 40 = 60 + 40 = 100

The length is 100 yards and the width is 60 yards.