Question

Sam and Charley have a rectangular swimming pool that is 8 feet wide and 14 feet long. They are going to build a tile border around the pool of uniform width. They have 75 square feet of tile. How wide is the border?

Answer 1

Answer:

The width of the border will be 3/2 ft or 1.5 ft

Step-by-step explanation:

The rectangular swimming pool is 8 ft wide and 14 ft long. A tile border is built around the pool of uniform width. The tile border is 75 ft².   The illustration below is just like a rectangle inside another rectangle.

The tile border around the pool has a uniform width. The width was added to both end of the length and the width of the rectangular pool.

Let

The added width = a

On both end the added width will be

(8 + 2a) and (14 + 2a)

The area of the whole rectangle formed including the border

(8 + 2a) (14 + 2a)

The area of the rectangular swimming pool

8 × 14 = 112  ft²

The area of the border(75 ft²)

(8 + 2a) (14 + 2a)  - 112  = 75

112 + 16a + 28a + 4a² - 112 = 75

4a² + 44a - 75 = 0

find the numbers you multiply to get -75 × 4 = -300 and also add to get 44. The numbers are - 6 and 50.

4a² - 6a + 50a - 75  = 0

2a(2a - 3) + 25(2a - 3) = 0

(2a−3)(2a+25)

2a - 3 = 0  or 2a + 25 = 0

a = 3/2 or a = -25/2

we will use a = 3/2 since it is positive.

The width of the border will be 3/2 ft or 1.5 ft