The area of a rectangle is 55 ft^2, and the length of the rectangle is 4 ft less than three times the width.

Question

The area of a rectangle is 55 ft^2, and the length of the rectangle is 4 ft less than three times the width.

Answer 1

Hi Bill, let x represent the width of the rectangle. Then 3x - 4 would represent the length. Using the formula for the area of a rectangle, we can find the values for the length and width.

 

Area of rectangle:

 

A = L * W

 

Substitute for A, L, and W:

 

55 = (3x - 4) * x

 

55 = 3x² - 4x

 

Move all terms to the same side of the equal sign:

 

3x² - 4x - 55 = 0

 

This can be factored:

 

(x - 5) * (3x + 11) = 0

 

Use the zero product rule to solve:

 

x - 5 = 0

 

x = 5

 

3x + 11 = 0

 

x = -11/3

 

We can discard the negative solution since the width cannot be negative.

 

The width of the rectangle is 5 feet. 

 

The length of the rectangle is 3 * 5 - 4, or 11 feet

 

Questions?

Answer 2

Width = 3x-4

 

length=x

 

area of rectangle = length*width

 

= x(3x-4)

 

= 3x^2-4x

 

55 =3x^2-4x

 

3x^2-4x-55=0

 

now solve the quadratic eq for x