A farmer wants to set aside a rectangular plot of land to contain 680 square meters?

A farmer wants to set aside a rectangular plot of land to contain 680 square meters. If the width is 9 less than the length, find the dimensions of the plot.

Length of the rectangular plot is 'x' say

Width of the 9 less then the length, so x - 9

Area of the rectangular plot is 680 square meters.

i.e. x(x - 9) = 680.

Distribute terms using distributive property:  a( b + c) = ab + ac

x2 - 9x = 680.

Subtract 680 from each side.

x2 - 9x - 680 = 0

Compare equation with standard from ax2 + bx + c = 0 and write the coefficients.

a = 1, b = -9 and c = - 680.

Quadratic formula x = [-b ± √(b2 - 4ac)]/2a

Substituting a = 1, b = -9 and c = - 680. in the Quadratic formula.

x = [-(-9) ± √((-9)2 - 4(1)(-680))]/2(1)

x = [9 ±√(81 + 2720)]/2

x = [9 ±√(2801)]/2

x = [9 ± 52.92]/2

x = [9 + 52.92]/2 or x = [9 - 52.92]/2.

x = 61.92/2 = 30.96

Therefore length x = 30.96 and width x - 9 = 30.96-9 = 21.96.

length = 30.96 and width = 21.96.