word problem

Question

Harold installed and built in rectangular pool measuring 15ft by 15ft. They want to add a decorative tile border of uniform width around all sides of the pool. How wide can they make the tile border if they purchased enough tile to cover 136 square feet?

Answer 1

Let x = the width of the border.  The area of the border is:

 

(15+x)² - 15² = 136

225 + 30x + x² - 225 = 136

x² + 30x - 136 = 0

 

Factors to:

 

(x+34)(x-4) = 0

x = -34 and 4

 

We can't have a negative width, so x = 4 ft

 

Check:

(15+x)²-15² = 136

(15+4)²-15² = 136

19² - 15² = 136

361 - 225 = 136

136 = 136

Check!