5.2.3 Solving Quadratic Equations by Factoring
Goal: Use factoring to solve geometric applications
Tutorial:
1. Whats the dimension of a rectangular
garden when the length is 5 feet more than the width of it and the area is 50
square feet?
Step
1: Label
Area: 50
ft2
Length:
(x+5)
Width:
(x)
Step
2: Make it into an equation
(x+5)(x)=50
Step
3: Solve equation
(x + 5)(x) = 50
x2
+ 5x =50 Simplify
x2
+ 5x 50 = 0 Write in standard form
(x
5)(x + 10) = 0 Factor
x
5 = 0 or x + 10 = 0 Use
zero property
x
= 5 or x = -10 Solve
for x
Step
4: Figure out the right
answer
x = 5 or
x = -10 ?
The answer cannot be negative because in reality a
garden cannot have a negative area, therefore the answer would have to be x =
5.
Step 5: Answer
the question
Since x = 5, the length of the garden would be 10ft.
and the width would be 5ft.
2. What are the dimensions of a rectangular
postcard whose length is 2 inches more than twice its width, with the area
being 40 inches squared?
Step 1: Label
Area: 40
Length:
(2x + 2)
Width:
(x)
Step 2: Make it into an equation
(2x + 2)(x) = 40
Step
3: Solve equation
(2x + 2)(x) = 40
2x2
+ 2x = 40 Simplify
2x2
+ 2x 40 = 0 Write in standard form
(2x
8)(x + 5) = 0 Factor
2x
8 = 0 or x + 5 = 0 Use
zero property
2x
= -8
x
= 4 x = -5 Solve for x
Step
4: Figure out the right
answer
The answer cannot be negative because nothing can have
a negative area, therefore the answer is x = 4.
Step 5: Answer
the question
Since x = 4, the length of the post card would be
10in. and the width would be 4in.
3. What are the dimensions of a triangular
sandbox if its length is 3 feet less than 6 times its height, with an area of
60 feet squared?
Step 1: Label
Area: 30
Length:
(6x 3)
Width:
(x)
Step
2: Make it into an equation
(6x 3)(x) = 60
Step 3: Solve equation
*Remember,
formula for area of a triangle is ½ · b · h
(6x
3)(x) = 60
2 (6x 3)(x)
= 60 · 2 Multiply
by 2 on both
2 sides
to cancel out the ½
(6x
3)(x) = 30
6x2
3x = 30 Simplify
6x2
3x 30 = 0 Write in standard form
(3x
6)(2x + 5) = 0 Factor
3x
6 = 0 or 2x + 5 = 0 Use
zero property
3x = 6 or 2x
= -5
x
= 2 or x = -1½ Solve
for x
Step
4: Figure out the right
answer
x = 2 or
x = -1½ ?
The
answer cannot be negative because nothing can have a negative area, therefore
the answer is x = 2.
Step 5: Answer
the question
Since
x = 2, the length of the sandbox would be 9ft. and the height would be 2 ft.
Now you try: (5.2 pg. 262
+92 94)
Find value of x.
92.
93.
94.
