Assignment:
(Quadratic Equations)
Part 1
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. Th shape is formed from two squares with side dimensions x and √x 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.
A. Write an expression for y in terms of x.
B. Write an expression for the area, A, of the garden, in terms of x.
C. If the area is 200 m2, find the dimensions of the garden.
Provide complete and step by step solution for the question and show calculations and use formulas.