Question

Michael is making a scale drawings a rectangular rooms using a scale of 1 in ratio 1 and 1/2 feet. He wants to use paper that has a width of 8 and 1/2 inches and a length of 11 inches for the drawings. Determine whether the scale drawings for each of these rims will fit on one piece of paper

Answer 1

To determine if scale drawings will fit on paper, the scale factor is applied to room dimensions to ensure they are smaller than the paper size. The examples provided illustrate how to calculate scale factors for various situations.

Step-by-step explanation:

Understanding Scale Drawings and Scale Factor

The problem presented involves creating scale drawings of rectangular rooms. The scale used by Michael is 1 inch to 1 and 1/2 feet. To determine if the scale drawings will fit on the paper size 8 and 1/2 inches by 11 inches, we need to apply this scale factor to the given dimensions of each room and ensure that the scaled dimensions are smaller than the paper size.

Let's review how to figure out each scale factor:

1. To convert 2 inches to 8 feet, we would use a scale factor of 1/48 (since 2/8 = 1/4 and 1 inch = 1/4 feet).
2. For 13 inches to 12 feet, the scale factor is 13/144 (or approximately 1/11.08).
3. 6 inches to 24 feet would have a scale factor of 1/48 (similar to the first example).

For scale problems, such as finding the scale factor for a rectangle or drawing, you would need to set up a proportion between the scale measurement and the actual measurement.

For example, to find the scale factor for a 2-inch wide rectangle that must be scaled down to a 9-inch wide rectangle, we would use the proportion 2/9, which gives us the scale factor of 2/9.

If we have a drawing of a man that is 4 inches high, and the actual man is 64 inches tall, the scale factor for the drawing would be 1/16 (since 4/64 reduces to 1/16).

Answer 2

Complete question is;

Michael is making scale drawings of rectangular rooms using a scale of 1 inch: 11/5 feet. He wants to use paper that has a width of 8 1/2 inches and a length of 11 inches for the drawings. Determine whether the scale drawings for each of these rooms will fit on one piece of paper.

Choose Yes or No for each set of dimensions.

a. 16 feet by 16 feet Yes/ No

b. 10 feet by 15 feet Yes/ No

c. 15 feet by 20 feet Yes/ No

d. 12 feet by 16 feet Yes/ No

Answer:

A) Yes

B) Yes

C) Yes

D) Yes

Step-by-step explanation:

We are told that 1 inch: 11/5 feet

This means in decimal form, 1 Inch represents 2.2 feet

A) 16 ft width gives: 16/2.2 inches = 7.27 inches

Also, 16ft length gives; 16/2.2 inches = 7.27 inches

Length and width are both less than the ones given in the question respectively. Thus, it's sufficient.

B) 10 ft width gives; 10/2.2 inches = 4.55 inches

15 ft length gives; 15/2.2 inches = 6.82 inches

Length and width are both less than the ones given in the question respectively. Thus, it's sufficient.

C) 15 ft width gives; 15/2.2 inches = 6.82 inches

20 ft width gives; 20/2.2 inches = 9.09 inches

Length and width are both less than the ones given in the question respectively. Thus, it's sufficient.

D) 12 ft width gives: 12/2.2 inches = 5.45 inches

16ft length gives; 16/2.2 inches = 7.27 inches

Length and width are both less than the ones given in the question respectively. Thus, it's sufficient.

Thus, all the dimensions are sufficient to fit on one piece of paper