Download Application Assignment #4

Dr. R. Bamman
Application Assignment #4
(Quadratic Equations)
Answer the following questions. Use Equation Editor to write mathematical expressions and
equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the
white space below each question to maintain proper formatting.
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. The shape is formed from two squares with side
dimensions x and x as shown.
x
x
Diagram not to scale
x
x
A.
Write an equation that represents the total area of the swimming pool surface.
The equation for area is A = x^2 + (√x)^2, that is A = x^2 + x
B.
The total area A is to be 30 m2. Write a quadratic equation that expresses this
information.
x^2 + x = 30
C.
Solve your equation in part B for the value of x. Find both of the solutions and show
all of your work.
x^2 + x = 30
x^2 + x - 30 = 0
x^2 + 6x - 5x - 30 = 0
Dr. R. Bamman
x(x + 6) - 5(x + 6) = 0
(x + 6)(x - 5) = 0
x = -6, 5
D.
Which of the solutions in part (c) is the correct value of x for the pool? State briefly
why you made this choice.
x = 5 gives the correct value of x
x = -6 is not valid because side length x cannot be negative.
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.
house
x
garden
y
The width of the garden is denoted by x, and the length by y.
A.
Write an equation that would represent the fencing she would be using to enclose her
garden using the given 50 meters. Write the equation as y in terms of x.(Solve for y)
(Hint: this is the perimeter)
x + x + y = 50
2x + y = 50
y = 50 - 2x
B.
Write an equation for the area, A, of the garden. Use your equation from Part A and
write the Area equation in terms of (x).
Dr. R. Bamman
A = xy
A = x(50 - 2x)
A = 50x - 2x^2
C.
If the area is 200 sq. meters, find the dimensions of the garden using your
equation from Part B. You can use any of the methods you have learned in the
course to solve your quadratic equation. Show all of your work.
50x - 2x^2 = 200
2x^2 - 50x + 200 = 0
2(x^2 - 25x + 100) = 0
x^2 - 25x + 100 = 0
x^2 - 5x - 20x + 100 = 0
x(x - 5) - 20(x - 5) = 0
(x - 5)(x - 20) = 0
x = 5, 20
When x = 5, y = 50 - 2(5) = 40
When x = 20, y = 50 - 2(20) = 10
The dimensions of the garden are: (a) Width = 5 m and Length = 40 m or (b) Width = 20 m and Length = 10 m.