Question

Valerie and Seth are measuring the outside walls of a house using two different instruments. They want to find the house's perimeter. Valeria measured the north and east sides while Seth measured the west and south sides. Their results are listed in the table.

Part A
Use decimal numbers to write an expression that represents the length of the walls that Valerie measured.

Part B
Now use decimal numbers to write an expression that represents the length of the wall that Seth measured.

Part C
Write an expression for the perimeter of the house. Use the work you completed in part A & B to guide you.

Part D
Simplify the expression from part C to find the perimeter of the house in feet.

Part E
Suppose that you evaluate the expression for Valerie's wall and the expression for Seth's wall separately. Then you add the two expressions together. Will you get the same answer that you arrived at in part D? Why or why not? Show your work to prove your case.​

PLEASE PLEASE PLEASE HELP I REALLY NEED HELP IN THIS WORK, THANK YOU.

Answer 1

The length of the walls Valerie and Seth measured can be found by adding the measurements of the respective sides. The perimeter of the house is the sum of the lengths of all four sides. Evaluating the expressions separately and adding them together will yield the same answer as finding the perimeter directly.

Step-by-step explanation:

Part A: The length of the walls Valerie measured can be represented by the sum of the measurements of the north and east sides of the house.

Part B: The length of the wall Seth measured can be represented by the sum of the measurements of the west and south sides of the house.

Part C: The perimeter of the house can be calculated by adding the lengths of all four sides together.

Part D: To find the perimeter of the house in feet, you would need to convert the measurements to feet if they are in a different unit. If the measurements are already in feet, you can simply add them together.

Part E: If you evaluate the expression for Valerie's wall and the expression for Seth's wall separately and then add them together, you will get the same answer as in part D, because the perimeter of the house is the same regardless of how it is measured.

Answer 2

A)

Valerie measured 4 walls at 2 1/2 feet. In decimal form, each wall is 2.5 feet long. So, the total length of the 4 walls is (2.5 × 4) feet.

Valerie measured 3 walls at 21 1/4 feet. In decimal form, each wall is 21.25 feet long. So, the total length of the 3 walls is (21.25 × 3) feet.

Valerie measured 1 wall at 32 feet.

The expression that gives the total length of the walls that Valerie measured is (2.5 × 4) + (21.25 × 3) + 32.

B)

Seth measured 1 wall at 3.5 feet.

Seth measured 2 walls at 22.75 feet. So, the total length of the 2 walls is (22.75 × 2) feet.

Seth measured 1 wall at 58 feet.

The expression that gives the total length of the walls that Seth measured is 3.5 + (22.75 × 2) + 58.

C)

The total length of Valerie’s walls is (2.5 × 4) + (21.25 × 3) + 32.

The total length of Seth’s walls is 3.5 + (22.75 × 2) + 58.

To find the expression for the perimeter of the house, add Valerie’s expression to Seth’s:

(2.5 × 4) + (21.25 × 3) + 32 + 3.5 + (22.75 × 2) + 58.

D)

(2.5 × 4) + (21.25 × 3) + 32 + 3.5 + (22.75 × 2) + 58

= 10 + 63.75 + 32 + 3.5 + 45.5 + 58

= 212.75

The perimeter of the house is 212.75 feet.

E)

The total length of Valerie’s walls is 105.75 feet:

(2.5 × 4) + (21.25 × 3) + 32 = 10 + 63.75 + 32 = 105.75 feet.

The total length of Seth’s walls is 107 feet:

3.5 + (22.75 × 2) + 58 = 3.5 + 45.5 + 58 = 107 feet.

The sum of 105.75 feet and 107 feet is 212.75 feet. The Commutative Property allows me to add numbers in any order. This is why the answers in parts D and E match.

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