The length of a rectangle is 11 ft more than twice the width and the area of the rectangle is 63 ft^2. Find the dimensions of the rectangle.

Question

Solving a word problem using a quadratic equation...

Answer 1

Maddie,

 

We know two things:

 

(1) length = 2*width + 11

 

l = 2w + 11

 

and 

 

(2) area = 63ft²

 

A = l * w = 63

 

Substitute the value of l in (1) for l in (2):

 

63 = (2w + 11) * w

 

63 = 2w² + 11w

 

0 = 2w² + 11w - 63

 

Factor the quadratic to find it's roots.

 

Using the quadratic formula, they are: 

 

w = 3.5, -9 (-9 doesn't work since the width cannot be negative)

 

width is 3.5ft

 

To find the length use (1) or (2) and substitute 3.5 for w:

 

(2) 63 = l * 3.5

 

l = 18 (length is 18 ft)

 

Hope this helps!

Answer 2

Let width = x

Let length = 2x + 11

 

Using these variables, create an equation for the area of a rectangle.

 

x(2x + 11) = 63

 

 

Distribute the x.

 

2x² + 11x = 63

 

 

Subtract 63 on both sides of equation.

 

2x² + 11x - 63 = 0

 

 

You now have a quadratic equation.  Solve for x from it to get your width.