1.
(05.01)
Mark wants to create a scale drawing of the poster shown below:
A rectangle is shown. The length of the rectangle is labeled 4 centimeters. The width of the rectangle is labeled 10 centimeters.
What are the dimensions of the poster at one-half its current size? (5 points)
2 cm by 10 cm
2 cm by 5 cm
8 cm by 20 cm
8 cm by 5 cm
The correct answer is 2 cm by 5 cm. When the poster is reduced to half its size, both the length and width are halved, resulting in a new dimension of 2 cm by 5 cm.
A poster is shown below:
A rectangle is shown. The length of the rectangle is labeled 18 inches. The width of the rectangle is labeled 6 inches.
What are the dimensions if the poster is enlarged by a factor of seven over two? (5 points)
42 in by 126 in
3 in by 9 in
9 in by 12 in
21 in by 63 in
To determine the dimensions of the poster if it is enlarged by a factor of seven over two, we need to multiply both the length and width by 7/2.
Length: 18 in * 7/2 = 63 in
Width: 6 in * 7/2 = 21 in
Therefore, the dimensions of the poster if it is enlarged by a factor of seven over two are 21 in by 63 in.
A window is 4 feet wide and 8 feet tall.
A rectangle is shown. The length of the rectangle is labeled 4 feet. The width of the rectangle is labeled 8 feet.
A manufacturer wants to use a scale factor of 1.5 to enlarge a window. What will the area of the window be after it is enlarged? (5 points)
32 ft2
48 ft2
52.25 ft2
72 ft2
To find the area of the window after it is enlarged by a scale factor of 1.5, we need to square the scale factor and then multiply it by the original area.
Original Area = 4 ft * 8 ft = 32 ft^2
Scale Factor = 1.5
Enlarged Area = (Scale Factor)^2 * Original Area
Enlarged Area = (1.5)^2 * 32 ft^2
Enlarged Area = 2.25 * 32 ft^2
Enlarged Area = 72 ft^2
Therefore, the area of the window after it is enlarged by a scale factor of 1.5 will be 72 ft^2.
A scale drawing of a game room is shown below:
A rectangle is shown. The length of the rectangle is labeled 2 inches. The width of the rectangle is labeled 4.5 inches. The scale is 1 to 30.
What is the area of the actual game room in square feet? Round your answer to the nearest whole number. (5 points)
9 ft2
23 ft2
56 ft2
270 ft2
To find the area of the actual game room, we need to convert the measurements from inches to feet and then scale it up by the scale factor.
Length: 2 inches * (1 foot/12 inches) = 0.1667 feet
Width: 4.5 inches * (1 foot/12 inches) = 0.375 feet
Now, we need to scale it up by a factor of 30:
Scaled Length: 0.1667 feet * 30 = 5 feet
Scaled Width: 0.375 feet * 30 = 11.25 feet
Now, we can calculate the area of the actual game room:
Area = Length * Width = 5 feet * 11.25 feet = 56.25 square feet
Rounding to the nearest whole number, the area of the actual game room is 56 square feet.
Therefore, the correct answer is 56 ft2.