Download The purpose of this lab is to practice multiplying, dividing

MAT 117 Application Assignment #1
Answer the questions below. Use Equation Editor when writing or solving
mathematical expressions or 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.
In order to receive credit, all work must be shown in the space provided. An
answer alone will not be sufficient.
The formulas that you will need are perimeter equals the sum of twice the length
and twice the width (P=2l+2w), and area equals the product of the length and the
width (A=lw).
Using the given floor plan above, answer the following questions.
Part 1: Using your knowledge of polynomial addition and subtraction (combining
like terms), answer the following questions.
1. Find the entire width of this two-bedroom apartment a (not counting the
patio) in terms of x. (Be careful to examine the expressions that are given
and use those to find the ones that are not.)
The 2x+5 is on the left and the x-3 fills in to the top on the right.
2x+5 + x-3
= 3x+2 feet
2. Find the entire length of this two-bedroom apartment in terms of x.
All from the bottom:
x + x+5 + x-1 + x + x+8
Simplify:
5x + 12 feet
Part 2: Using your knowledge of the distributive property and polynomial addition
and subtraction, answer the following questions. (Remember, P=2l+2w.)
3. Find the perimeter of the entire 2-bedroom apartment (excluding the patio)
in terms of x.
P = 2L + 2W
= 2(3x+2) + 2(5x+12)
= 6x + 4 + 10x + 24
= 16x + 28 feet
4. Find the perimeter of the living room and dining room in terms of x.
Width = 2x+5
Length = x+x+5 = 2x + 5
Perim = 2(2x + 5) + 2(2x + 5)
= 4x + 10 + 4x + 10
= 8x + 20 feet
Part 3: Using your knowledge of solving linear equations, answer the following
questions.
5. If the perimeter of the living room and dining room is 68 feet, what is the
value of x?
Set the previous answer equal to 68:
68 = 8x + 20
Subtract 20:
48 = 8x
Divide by 8:
x = 6 feet
6. If the length of the entire apartment is 52 feet, what is the value of x?
Using the value from problem 2:
52 = 5x + 12
Subtract 12:
40 = 5x
Divide by 5:
x = 8 feet
Part 4: You have reviewed polynomial multiplication and division in this module,
practice now. (Remember, A=lw)
7. Find the equation that would represent the area of the entire living
room/dining room in terms of x.
L*W
= (2x+5)(2x+5)
Using the rule for perfect square trinomials:
Area = 4x2 + 20x + 25 square feet
8. Find the equation that would represent the area of the entire apartment
(excluding the patio) in terms of x. Note: don't forget to subtract for the
cutout area in the upper left corner.
= L*W – Lsmall * Wsmall
= (3x+2)(5x+12) – (x-3)(x-3)
FOIL
= 15x2 + 36x + 10x + 24 – (x2 – 6x + 9)
Simplify:
Area = 14x2 + 52x + 15 square feet
9. If the area of the kitchen was 2x-4, what would be the width? Write the
expression or number for the width.
Area = L*W
2x-4 = (x-2)W
Factor:
2(x-2) = (x-2)W
Divide out the x-2:
W = 2 feet
10. If the area of the dining room and living room is 225 sq. ft., what is the
equation that would be used to solve for x? Write the equation with zero
on the right and then solve for x.
Set that area to 225:
4x2 + 20x + 25 = 225
Subtract 225:
4x2 + 20x – 200 = 0
Divide by 4:
x2 + 5x – 50 = 0
Factor:
(x+10)(x-5) = 0
x = -10 or 5, but it can’t be negative, so:
x = 5 feet