The area of a rectangle is 28. The length is one foot greater then twice the width whats the length

Question

Hannah has finshed knitting a blanket. She wanted the length of the blanket to be 1 foot greater than twice the width, beacuse otherwise her toes get cold.If the area covered by the blanket is 28 square feet, how long is the blanket

Answer 1

Let the width be x ft

Then the length will be (2x + 1) ft

 

The quadratic eq will be

 

x(2x+1) = 28

2x²+x-28=0

2x²+8x-7x-28=0

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

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

 

The two solutions of x are:

x=-4 and x=3.5 ft

In this situation, the negative answer is not applicable.

 

So the width is 3.5 ft

The length is 2x+1 = (2*3.5)+1= 8 ft

For sanity check area = 3.5*8 = 28 sq. ft

 

Hope this helps