Question

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 1

a) Yes

b) Yes

c) Yes

d) Yes

Explanation:

8½ inches --> 17/2 × 11/5 = 18.7 feet

11 inches --> 11 × 11/5 = 24.2 feet

a. 16 feet by 16 feet Yes

b. 10 feet by 15 feet Yes

c. 15 feet by 20 feet Yes

d. 12 feet by 16 feet Yes

Answer 2

all will fit

Explanation:

We can use ratios to solve

Changing 11/5 into a decimal

1 inch x

-------------- = -----------

2.2 ft 16 ft

Using cross products

16 = 2.2 x

Divide each side by 2.2

16/2.2 = x

7.2727 =x Since this is less than 8.5 inches Yes

1 inch x

-------------- = -----------

2.2 ft 15 ft

Using cross products

15 = 2.2x

Dividing each side by 2.2

6.8 =x

Yes

1 inch x

-------------- = -----------

2.2 ft 20 ft

Using cross products

20 = 2.2x

9.09 =x

If this is the 11.5 inch side (15 ft is 6.8 inches which is less than 8.5 inches)

yes

1 inch x

-------------- = -----------

2.2 ft 12 ft

12 = 2.2x

5.4 inches yes since 16 is 6.8 inches