Determine algebraically the dimensions of the soccer field in yards.

Question

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

Answer 1

Area is 6000 yd²

LW = 6000

 

field must be 40 yards longer than its width

L = W + 40

 

Replace L with W+40 in 1st equation to solve for Width

 

(W+40)(W) = 6000

W² + 40W - 6000 = 0

This is a quadratic but is factorable

Factors of -6000 that add to 40 are (100)(-60)

(W+100)(W-60) = 0

 

W = -100   or   W = 60

Since the width will not be negative discard -100

 

The width is 60 yards

Length is W+40 = 100 yards