Answer:

width = 5

length = 11

Step-by-step explanation:

let x = width

3x - 4 = length

55 = Area

Solution:

A = LW

55 = (3x - 4) x

55 = 3x^2 - 4x

3x^2 - 4x - 55 = 0

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

3x + 11 = 0 x - 5 = 0

3x = -11

1/3 ( 3x) = -11(1/3) x = 5

x = -11/3

hence, we will use x = 5 since we cannot use a negative number as dimension of sides of polygon.

therefore, width = 5

length = 3x - 4

length = 3(5) - 4

length = 15 - 4

length = 11

Answer:

Hi Jhounsanfreianpiloto, 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