How to find area around rectangle perimeter?

Question

A rectangular garden has dimensions 23 feet by 16 feet. A gravel path of equal width is to be built around the garden on the outside. How wide can the path be if there is enough gravel for 490 square feet?

Answer 1

Let X= width of path around 

 

Inner area = 23x16 sq ft

Outer area = (23+2X) x (16 +2X)

 

Difference= (outer area - inner area) = 490 sq ft Given

Which gives

 

4X² +78 X -490 = 0

             

Solving for X

 X = -49/2 ft and X = 5 ft  

-ve value can be ignored 

So width of path = 5 ft