A community is developing plans for a pool and hot tub. The community plans to form a swim team, so the pool must be built to certain dimensions. Answer the questions to identif…

Question

Answer each question individually
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A community is developing plans for a pool and hot tub. The community plans to
form a swim team, so the pool must be built to certain dimensions. Answer the
questions to identify possible dimensions of the deck around the pool and hot tub.

Part I: The dimensions of the pool are to be 25 yards by 9 yards. The deck will be
the same width on all sides of the pool. Including the deck, the total pool area
has a length of (x+25) yards, with a width of (x+9) yards.

a.) write an equation, representing the total area of the pool and the pool deck. Use white represent the total area. Hint: the area of a rectangle is the length times width

b.) re-write the area equation in standard form. Hint: use the FOIL method.

c.) re-write the equation from part B in vertex form by completing the Square. Hint: move the constant to the other side, add to each side, rewrite the right side as a perfect square trinomial, and finally, isolate the Y.

d.) what is the vertex of the parabola? What are the X - and Y - intercepts? Hint: use your answer from part a to identify the X – intercepts. Use your answers from part B to identify the Y – intercept. Use your answer from part C to identify the vertex.

e.) grab the para bola. Use the key features of the graph that you identified in part D.

f.) in this problem, only positive values of X makes sense why?

g.) what point on your graph shows a total area that includes the pool but not the pool deck?

h.) the community decided on a pool area that add 6 yards of pool deck to both the length and the width of the pool. What is the total area of the pool and deck when X=6 yards?

Part ll

A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by X feet of deck on each side. The enclosed space is also square that has an area of 169 ft.². Find the width of the deck the space around the hot tub, x.

Step 1-Ryan equation for the area of the enclosed space in the form Y=(side length)2 hint: don’t forget to add x to each side of the hot tub

Step 2- substitute the area of the enclosed space for y in your equation


Step 3- so if your equation from part B for X

Step 4: what is the width of the deck around the hot tub? Hint : one of the answers from part seat is not reasonable

Answer 1

You have a rectangle around a rectangle. Since you have

the pool plus deck as having length = (x+25) and width = (x+9)

then x is twice the width of the deck. However, the equation for the total area of pool and deck is still area = length*width

y = (x+25)(x+9)

y = x2 + 9x + 25x + 225

y = x2 + 34x + 225 where x represents twice the width of the deck