Question

A rectangular vegetable garden will have a width that is 4 feet less than the length, and an area of 140 square feet. If x represents the length, then the length can be found by solving the equation:

x(x-4)= 140

What is the length, x, of the garden?

The length is blank feet.

The solution is

Answer 1

The length of the garden=14 feet

Explanation:

Step 1: Determine the dimensions of the garden

length of the garden=x feet

width of the garden=(x-4) feet

Step 2: Determine the area of the garden

Area of the garden=length×width

where;

area=140

length=x

width=x-4

replacing'

x(x-4)=140

x²-4x-140=0, solve the quadratic equation;

x={-b±√(b²-4ac)}/2a

x={4±√4²-4×1×-140}/2×1

x={4±√(16+560)}/2

x={4±√576}/2

x=(4±24)/2

x=(4+24)/2=14, or (4-24)/2=-10, take x=14

The length=14 feet, width=(14-4)=10 feet

The length of the garden=14 feet