Question

3 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 the actual lengths of the garden

Given the first scale \(8\mathrm{ft}:1\mathrm{cm}\).
For the height of the first drawing \(h_1 = 3.6\mathrm{cm}\), the actual height \(H\) of the garden:
Since \(\frac{\text{Actual length}}{\text{Drawing length}}=\frac{8\mathrm{ft}}{1\mathrm{cm}}\), then \(H=3.6\times8 = 28.8\mathrm{ft}\)
For the base of the first drawing \(b_1 = 2.4\mathrm{cm}\), the actual base \(B\) of the garden:
\(B = 2.4\times8=19.2\mathrm{ft}\)

Step2: Find the lengths in the second - scale drawing

Given the second scale \(2\mathrm{ft}:1\mathrm{cm}\).
For the base \(B = 19.2\mathrm{ft}\), let the base length in the second - scale drawing be \(b_2\).
Using the proportion \(\frac{B}{b_2}=\frac{2\mathrm{ft}}{1\mathrm{cm}}\), then \(b_2=\frac{19.2}{2}=9.6\mathrm{cm}\)
For the height \(H = 28.8\mathrm{ft}\), let the height length in the second - scale drawing be \(h_2\).
Using the proportion \(\frac{H}{h_2}=\frac{2\mathrm{ft}}{1\mathrm{cm}}\), then \(h_2=\frac{28.8}{2}=14.4\mathrm{cm}\)

Answer:

D. \(9.6\mathrm{cm}\) and \(14.4\mathrm{cm}\)