Length and width

Question

The length of a rectangle is
1 ft
more than double the width, and the area of the rectangle is
28 ft2
. Find the dimensions of the rectangle.

Answer 1

L x W = Area

L = 2W +1

Substitute for L:

(L x W) = 28

(2W + 1)(W) = 28, distribute

2W² + W = 28

2W² + W -28 = 0

(2W - 7)(W + 4) = 0, solve for each

2W = 7 so W = 3.5 and

W = -4 (not a solution)

Thus, width is 3.5 feet and the length is (2W + 1) = (2)(3.5) + 1 = 8ft

Area = (8ft) x (3.5ft) = 28 ft²

 

Answer 2

area of a rectangle = L x W 

 

we know that L x W = 28 sq. ft 

but since L = 2 * W, then L x W = ((2 * W)+1) * W = 2 * W²  + W = 28 sq. ft 

 

if W = x, 

this sets up the quadratic equation 2x² + x - 28 = 0 

 

plugging this into the quadratic formula, where a=2, b=1 and c = -28

 

x = [-b +/- sqrt(b^2 - 4ac)] / 2a = [-1 +/- sqrt(1 + 4 * 2 * 28)] / 4 = [-1 +/- sqrt(225)] / 4 = (-1 +/- 15) / 4

 

the only positive solution is x = 3.5 = W 

 

then the width is 3.5 feet, and the length is 8 feet. note that 3.5 * 8 = 28

Answer 3

Hi Dana, let x represent the width. Then the length would be 2x + 1. We can use the formula for the area of a rectangle: 

 

    L * W = A

 

to find the length and width of the rectangle.

 

Substitute for L, W, and A in the formula:

 

(2x + 1) * x = 28

 

2x² + x = 28

 

Subtract 28 from both sides:

 

2x² + x - 28 = 0

 

Solve for x:

 

(2x - 7) * (x + 4) = 0

 

Use the zero product rule to find the value of x:

 

Solution - 2x - 7:

 

2x - 7 = 0

 

Add 7 to both sides:

 

2x = 7

 

Divide both sides by 2:

 

x = 3.5, one solution.

 

Solution - x + 4:

 

x + 4 = 0

 

Subtract 4 from both sides:

 

x = -4

 

We can discard this solution. the width of the rectangle must be greater than 0.

 

If the width of the rectangle is: 3.5 feet, the length will be 2 * 3.5 + 1, or 8 feet.

 

Check:

 

3.5 * 8 = 28

 

28 = 28, values check.

 

Questions?