Section D Practice Problems

Problem 1

An author takes a 4-hour airplane flight for a work trip. The plane flies 478 miles each hour. How many miles does she travel?
A photographer takes a 4-hour drive for his work trip. The car travels 57 miles each hour. How many miles does he travel?
How many miles further did the author travel than the photographer?

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Solution

Sample response:

$4 \times 478 = 1,912$
$4 \times 57 = 228$
$1,912 - 228 = 1,684$

Problem 2

The diagram shows the side lengths of a sports field.

What is the perimeter of the field? Explain or show your reasoning.
What is the area of the field? Explain or show your reasoning.

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Solution

256 meters. There are two sides of 85 meters, so that's 170 meters. The other two sides are 43 meters each, so that’s 86 meters more. The perimeter is $170 + 86$ or 256 meters.
The area is $85 \times 43$ or 3,655 square meters.

Problem 3

The table shows the number of students who have different numbers of pets at a school.

How many pets do all the students have together? Explain or show your reasoning.

number of pets	number of students
1	218
2	167
3	287
4	138

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Solution

1,965 pets. Sample response:

$1 \times 218 = 218$

$2 \times 167 = 334$

$3 \times 287 = 861$

$4 \times 138 = 552$

In total, the students have $218 + 334 + 861 + 552$ or 1,965 pets.

Problem 4

A builder covers the floor of a rectangular room that is 23 feet by 25 feet with tiles that are 1 foot by 1 foot. The tiles are sold in boxes of 12.

Diego says 59 boxes are needed to cover the floor, and there will be a few leftover tiles.

Is Diego's answer reasonable? Explain or show your reasoning.
How many boxes of tiles would you buy to cover this floor? Explain or show your reasoning.

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Solution

No. 59 boxes would be too many. Sample response: The area of the room is $23 \times 25$ or 575 square feet. $59 \times 10$ is already 590, and then there is an additional 2 tiles or 2 square feet per box, which means $59 \times 2$ or 108 extra tiles.
Sample response: 48 boxes. I know $50 \times 12$ is 600, and 600 is 25 more than 575. If I get 2 boxes fewer than 50, it’d mean 24 tiles ( $2 \times 12 = 24$ ) fewer than 600, which is 576 tiles or 576 square feet and 1 more than 575. There will be 1 extra tile.

Problem 5

Find a rectangular room at home or in the school.

Choose inches, feet, or yards to measure the length and width of the room. Explain your reasoning.
Measure the length and width to the nearest whole number.
Find the perimeter and area of the room.
Can you find a length and width pair for a room that has the same perimeter but a different area?
Can you find a length and width pair for a room that has the same area but a different perimeter?

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Solution

Sample responses:

I would choose to use feet. If I use inches, the measurements would be in the hundreds and harder to multiply. If I use yards, I may have to round up or down a lot to the nearest whole numbers, so the perimeter and area won’t be precise.
The living room in my home is rectangular. It is 14 feet wide and 15 feet long.
The perimeter is 58 feet and the area is $14 \times 15$ or 210 square feet.
Yes, a room that is 13 feet by 16 feet would also have a perimeter 58 feet, but the area would be $13 \times 16$ or 208 square feet.
Yes, a room that is 10 feet by 21 feet would have an area of 210 square feet, and a perimeter of 62 feet.

Problem 6

The area of a rectangle is 720 square centimeters. One side is 6 centimeters longer than the other. What is the perimeter of the rectangle? Explain or show your reasoning.

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Solution

108 centimeters. Sample response: I need to find two numbers that multiply to 720 and where one of the numbers is 6 more than the other. I tried $72 \times 10$ and $36 \times 20$ and these are too far apart. Since $72 = 24 \times 3$ , that means $720 = 24 \times 30$ and 30 and 24 are 6 apart. So the length and width of the rectangle can be 30 centimeters and 24 centimeters. Its perimeter is $2 \times 54$ or 108 centimeters.