Question

the scale from a garden to this drawing is 8 ft to 1 cm. the scale from the same garden to another drawing is 2 ft to 1 cm. what are the lengths of the base and height of the garden in the other scale drawing? a 0.6 cm and 0.9 cm b 1.2 cm and 1.8 cm c 4.8 cm and 7.2 cm d 9.6 cm and 14.4 cm kamal chose a as the correct answer. how might he have gotten that answer?

Explanation:

Step1: Find actual lengths of garden

The first - scale is 8 ft to 1 cm. The base in the first - scale drawing is 2.4 cm and the height is 3.6 cm.
The actual base length $b_{actual}=2.4\times8 = 19.2$ ft and the actual height length $h_{actual}=3.6\times8 = 28.8$ ft.

Step2: Find lengths in the second - scale drawing

The second - scale is 2 ft to 1 cm.
The base length in the second - scale drawing $b_{new}=\frac{19.2}{2}=9.6$ cm.
The height length in the second - scale drawing $h_{new}=\frac{28.8}{2}=14.4$ cm.

Step3: Analyze Kamal's error

Kamal might have divided the lengths in the first - scale drawing by 4 instead of multiplying by 4 (since the new scale is $\frac{8}{2}=4$ times more "zoomed - in" compared to the first scale). He did $2.4\div4 = 0.6$ cm for the base and $3.6\div4 = 0.9$ cm for the height.

Answer:

The correct answer is D. 9.6 cm and 14.4 cm. Kamal might have divided the base and height lengths in the first - scale drawing by 4 instead of using the correct scale - factor relationship.