A 15 -ft by 15 -ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 136 ft2 , how wide is the walkway?

2ft wide

Step-by-step explanation:

Total Area = Area of the summing pool + total Area of the walkway.

Area of the summing pool = 15 * 15 = 225ft²

And total area of walkway = 136ft²

∴ total area = 225 + 136 = 361 ft².

Let w = The width of the walkway.

Since the walkway has a uniform width

∴ Total Area of pool and walkway = (15+2w) (15+2w)

⇒ (15+2w) (15+2w) = 361 ... (1)

Expanding Equation (1)

15*15 + 15*2w + 2w*15 + 2w*2w = 361

⇒ 225 + 30w + 30w + 4w² = 361 ... (2)

Rearranging equation (2) above and collecting like terms

4w²+60w = 361-225

4w² + 60w = 136 ... (3)

Dividing all through equation (3) by 4

4w²/4 + 60w/4 = 136/4

w² + 15w = 34 ... (4)

rearranging equation (4)

w²+15w - 34 = 0

Using factorization method to solve the quadratic equation,

w² + 15w - 34 = 0

Two numbers whose sum give + 15 and whose product gives - 34

are + 17 and - 2.

∴ w² - 2w + 17w - 34 = 0

grouping the equation,

(w²-2w) + (17w-34) = 0

Bringing out the common terms in both bracket.

w (w-2) + 17 (w-2) = 0

since both term in the bracket are the same, take one of the term in the bracket and form a bracket for the outer term i. e

(w-2) (w+17) = 0.

Either w-2 = 0

w=+2

OR w+17 = 0

w=-17.

The right answer is w=+2 as wide can not be negative.

∴ The walkway is 2ft wide.