The area of a rectangle is 54 square feet. The height is three more than twice the width. Find the width of the rectangle.

4.5 ft

Step-by-step explanation:

Let length = 2x + 3

Let width = x

Area = 54 ft2

length × width = Area

x(2x + 3) = 54

2x2 + 3x = 54

2x2 + 3x - 54 = 0

(2x - 9)(x + 6) = 0

x = 9/2    and    x = -6

x = 4.5    and    x = -6

We accept x = 4.5 because length cannot be a negative value.  Substituting this value into the dimensions:

width = 4.5 ft

length = 2(4.5) + 3 = 9 + 3 = 12 ft

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.