Question

1. for a school project, frank created a scale drawing of the cover of the book he was reading. his drawing was a rectangle that was 1.5 centimeters by 2.0 centimeters. which of the following can be the dimensions of the original book cover? show all work to prove your answer.

a. 22.5 cm × 40.0 cm
b. 18 cm × 24 cm
c. 16 cm × 24 cm
d. 19.5 cm × 20.0 cm

1. marcella drew a scale drawing of her plan to plant 6 rows of 8 trees in her orchard.

orchard
chart of orchard with width = 70 m, length = 50 m, and trees
marcella used a 7 - inch - wide rectangular grid for the drawing. what is the scale marcella used for her drawing?

Explanation:

Problem 2

Step1: Find the ratio of original to drawing

First, we need to find the scale factor by checking the ratio of each option's dimensions to the drawing's dimensions (1.5 cm by 2.0 cm). For a scale drawing, the ratio of corresponding sides should be equal (scale factor).

Step2: Check Option A

For A: \( \frac{22.5}{1.5} = 15 \), \( \frac{40.0}{2.0} = 20 \). Ratios are 15 and 20 (not equal).

Step3: Check Option B

For B: \( \frac{18}{1.5} = 12 \), \( \frac{24}{2.0} = 12 \). Ratios are both 12 (equal).

Step4: Check Option C

For C: \( \frac{16}{1.5} \approx 10.67 \), \( \frac{24}{2.0} = 12 \). Ratios not equal.

Step5: Check Option D

For D: \( \frac{19.5}{1.5} = 13 \), \( \frac{20.0}{2.0} = 10 \). Ratios not equal.

Step1: Identify known values

The actual width of the orchard is 70 m, and the drawing width is 7 inches.

Step2: Calculate the scale

Scale is drawing length : actual length. So, \( 7 \text{ inches} : 70 \text{ meters} \). Simplify by dividing both by 7: \( 1 \text{ inch} : 10 \text{ meters} \).

Answer:

B. 18 cm x 24 cm

Problem 3