You have a pool that measures 8 yards by 10 yards. You want to build a deck around all four sides of the pool and you want to increase the total area to 120 square yards. The deck is the same width on both sides forming a perfect rectangle. What is the width of the deck?

Question

anonymous · Answer

Let x be the width of the deck. The length & width of the pool and deck combined becomes: 

l = 10 + 2x 
w = 8 + 2x 

Draw yourself a picture and you'll see where the "+ 2x" part came from in each of those statements. 

You want to increase the total area (i.e. defined by the outer dimensions of the deck) to 120 sq yd. 

A = lw 
120 = (10 + 2x)(8 + 2x) 
120 = 80 + 36x + 4x^2 
0 = 4x^2 + 36x - 40 
0 = 4(x^2 + 9x - 10) 
0 = x^2 + 9x - 10 
0 = (x + 10)(x - 1) 

So either x=-10 (which is impossible since the deck cannot have negative width), or x=1. So the deck is 1yd wide.