Those are square roots with x in diagram above for part one. Diagram for part tw
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Those are square roots with x in diagram above for part one.
Diagram for part two.
Mrs. Thomas wants to do some renovations to her backyard. She wants to get a swimming pool built in the shape of the letter L. The shape is formed from two squares with side dimensions x and as shown. A. Write down an expression for the area of the swimming pool surface. B. The area A is to be 30 m2. Write a quadratic equation that expresses this information. C. Find both the solutions of your equation in part (b). Show all work. D. Which of the solutions in part (c) is the correct value of x for the pool? State briefly why you made this choice. Part 2 Mrs. Thomas also has a garden in her yard and wants to put a 50-meter rectangular fence around it. She only needs to fence in 3 sides because the other side is alongside the house. The width of the garden is denoted by x, and the length by y.Explanation / Answer
Part1 a) The area of the "L" shaped swimming pool will be the sum of the areas of the two squares. Area of square = s^2 Area of large square (dimensions of x by x) = x^2 Area of small square (dimensions sqrt(x) by sqrt(x) = (sqrtx)^2 = x Total area of swimming pool: x^2 + x b) area of swimming pool should be 30 m^2 x^2 + x = 30 c) x^2 + x = 30 [put in standard form] x^2 + x - 30 = 0 [factor the equation] (x+6)(x-5) = 0 [solve each term] x = -6 OR x = 5 d) the answer for x needs to be x = 5. You cannot have a dimension of a pool being negative therefore x = -6 is not a viable solution PartII a) P = 2x + y [only three sides because one side is by the house] 50 = 2x + y y = 50 - 2x b) Area = x(y) Area = x(50-2x) Area = 50x - 2x^2 c) 200 = 50x - 2x^2 2x^2 - 50x + 200 = 0 x^2 - 25x + 100 = 0 (x - 20)(x-5) = 0 x = 20 or x = 5 x = 20 and y = 10 or x = 5 and y = 40
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