Question

math homework: scale drawings day 1
shemar, jalil and andres are drawing cartoons for the 8th grade yearbook. they make a sketch of a large poster, shown below:
(there are two images: a large poster of a cartoon character with width 12 feet and height 20 feet, and a sketch of the same character with a part labeled 6 cm, and parts labeled a (width) and b (height) for the sketch.)

1. show work to determine the length of a & b:

a)
b)

1. what scale factor did the boys use to create their sketch? explain how you know.

Explanation:

Step1: Find scale factor

First, convert poster's 9 ft to cm: $9 \text{ ft} = 9 \times 30.48 = 274.32 \text{ cm}$.
Scale factor $= \frac{\text{Sketch height}}{\text{Poster height}} = \frac{6}{274.32} = \frac{1}{45.72}$

Step2: Calculate length A

Poster width: $12 \text{ ft} = 12 \times 30.48 = 365.76 \text{ cm}$
$A = 365.76 \times \frac{1}{45.72} = 8 \text{ cm}$

Step3: Calculate length B

Poster total height: $20 \text{ ft} = 20 \times 30.48 = 609.6 \text{ cm}$
$B = 609.6 \times \frac{1}{45.72} = 13.33 \text{ cm}$ (or $\frac{40}{3} \text{ cm}$)

Step4: Confirm scale factor

Scale factor is $\frac{1}{45.72}$ (or $\frac{1 \text{ cm}}{4.572 \text{ ft}}$), derived by matching the known corresponding height of the lower section (6 cm sketch to 9 ft poster, converted to cm for consistent units).

Answer:

A) Length $A = 8$ cm
B) Length $B = \frac{40}{3} \approx 13.33$ cm
Scale factor: $\frac{1}{45.72}$ (or $\frac{1\text{ cm}}{4.572\text{ ft}}$), calculated by dividing the sketch's known 6 cm height by the poster's corresponding 9 ft (274.32 cm) height to get the ratio of sketch size to actual poster size.