I need help

Question

Judy has a rectangular garden 12 by 26 feet. She wants to put a grass border around the garden with a uniform width on all sides. If she has enough grass seed to cover 264 square feet, how wide can the grass border be?

Answer 1

Let w be the uniform width for the border.

 

Including the garden the dimensions of the garden and border would be (12 + 2w) by (26 + 2w), which is an area

A = (12 + 2w) * (26 + 2w) = 312 + 24w + 52 w + 4w² = 4w² + 76w + 312

 

Subtracting the area of the garden leaves the area for the grass border to be (4w² + 76w) which is the same as the

amount seed to cover 264 square feet.

 

4w² + 76w = 264

 

Dividing through by 4 this is the same as w² + 19w -66 = 0

 

Now w² + 19w - 66 = (w - 3) * (w + 22 ) = 0

 

The border must be 3 feet wide.  The other solution is -22 which is negative and can not be the value for the border.