A pool is surrounded through a deck that has the similar width all the way around. The total area of the deck only is 400 square feet. The dimensions of the pool are 18 feet through 24 feet. How many feet is the width of the deck?
Let x = the width of the deck. Because the width of the pool only is 18, the width of the pool and the deck is x + x + 18 or 2x + 18. Since the length of the pool only is 24, the length of the pool and the deck mutually is x + x + 24 or 2x + 24. The total area for the pool and the deck together is 832 square feet, 400 square feet added to 432 square feet for the pool. Area of a rectangle is length times width so multiply the expressions together and set them equal to the total area of 832 square feet: (2x + 18)(2x + 24) = 832. Multiply the binomials using the distributive property: 4x2 + 36x + 48x + 432 = 832. Combine such as terms: 4x2 + 84x + 432 = 832. Subtract 832 from both sides: 4x2 + 84x + 432 - 832 = 832 - 832; simplify: 4x2 + 84x - 400 = 0. Factor the trinomial completely: 2(2x2 + 42x - 200) = 0; 2(2x - 8)(x + 25) = 0. Set every factor equal to zero and solve: 2 ≠ 0 or 2x - 8 = 0 or x + 25 = 0; x = 4 or x = -25. Reject the negative solution since you will not have a negative width. The width is 4 feet.