Question

A rectangular vegetable garden will have a width that is 3 feet less than the length, and an area of 54 square feet. if x represents the length, then the length can be found by solving the equation: x(x−3)=54x(x-3)=54 what is the length, x, of the garden? the length is _____ feet.

Answer 1

Length of rectangular garden = x feet

As, Width is 3 feet less than Length.

Width = (x-3 ) feet

Area of Rectangle = Length × Breadth

Area = 54 square feet

→54 = x × (x-3)

→ x²-3 x-54=0

Splitting the Middle term

→x² - 9 x + 6 x- 54=0

→x × (x-9)+6 × (x-9)=0

→ (x+6)(x-9)=0

→x+6=0 ∧ x-9=0

x≠-6, as length can't be negative.

So, x=9

Length of Rectangular garden = 9 feet

Answer 2

To determine the length of the rectangular flower garden, we need to derive equations from the given measurements and relations. The given measurements are the area, and the relation of the width and the length. From these, we generate the equation needed. We do as follows:

Area = Length x Width

where length = x ft
width = x - 3 ft
area = 54 ft^2

54 ft^2 = x ft (x -3) ft
54 ft^2 = x^2 - 3x ft^2

Solving for the value of x, we will have two values which are
x = -6 ft ( NOTE: this value can't be the answer since we cannot have a negative value for the length)
x = 9 ft = length