A pool measures 15 feet by 17 feet. A cement walkway is added around the pool, to both the width and the length. The area of the pool and the cement walkway is now 483 square feet. What is the width of the cement walkway?

3 feet

Step-by-step explanation:

The diagram showing the pool and the walkway has been attached to this response.

The area of the pool = 15feet x 17 feet = 255 square feet

The total area of the pool and the walkway = 483 square feet

The area of the walkway is the difference between the total area and the area of the pool. i.e

Area of walkway = total area - area of pool

Area of walkway = 483 - 255 = 228 square feet

Now, from the diagram, the walkway can be seen as four rectangles - A, B, C and D - all with a width of x.

Area of rectangle A = (17 + 2x) * x = 17x + 2x²

Area of rectangle B = (17 + 2x) * x = 17x + 2x²

Area of rectangle C = 15 * x = 15x

Area of rectangle D = 15 * x = 15x

Area of walkway = Area of rectangle A + Area of rectangle B + Area of rectangle C + Area of rectangle D

228 = [17x + 2x²] + [17x + 2x²] + [15x] + [15x]

228 = 64x + 4x²

4x² + 64x - 228 = 0

Divide through by 4

x² + 16x - 57 = 0

Now let's solve the quadratic equation:

x² - 3x + 19x - 57 = 0

x(x - 3) + 19(x - 3) = 0

x - 3 = 0     or     x + 19 = 0

x = 3          or      x = -19

Since width cannot be negative, the correct solution is x = 3

Therefore, the width of the walkway is 3 feet

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

df =

both have same length