what are the dimensions?

Question

The length of a rectangle is 4 meters less than twice the width. If the area of the rectangle is 336 square​ meters, find the dimensions.

Answer 1

Width is 14 m and Length is 24 m

Answer 2

First set up the sides of the rectangle: Let x be the width of the rectangle. If the length is 4 meters than twice the width we can use the following expression to represent the length: 2x - 4. (remember x stands for the width of the rectangle.

Area of a rectangle is length x width so all we need to do is plug in our expressions:

l x w = A

(2x-4)(x) = 336

now distribute on the right side

2x^2 -4x = 336

We can see that we have a quadratic now, so we need to get everything on one side of the equation:

2x^2 - 4x -336 = 0

To solve for x first pull out the greatest common factor, which is 2

2 (x^2 - 2 - 168) = 0

At this point, we have options. We could try to factor or we could use the quadratic formula. I decided to factor. I am looking for a factor pair that multiplies to -168 and adds to -2. One factor must be negative to accomplish this:

2 (x - 14) (x + 12) = 0

Last step is to solve for the zeros. Set each ( ) equal to zero and solve for x:

x - 14 = 0 x + 12 = 0

x = 14 x = -12

x (the width) is 14 because you cant have negative dimensions

now you solve for the length using the expression we made earlier

2x - 4 = length

2(14) -4 = 28-4 = 24

The dimensions of the rectangle are 14 meters by 24 meters.