Question

1.3.2 test (cst): science and engineering
question 24 of 25
a horticulturist is planning a garden that is 1 m × 3 m. she uses a model to plan it. which dimensions could she use to make a scale model?
a. 16 cm × 36 cm
b. 50 cm × 100 cm
c. 1 m × 2 m
d. 0.5 m × 1.5 m

Explanation:

Step1: Understand scale model ratio

A scale model should maintain the same ratio as the original. The original garden is \(1\,\text{m} \times 3\,\text{m}\), so the ratio of length to width is \(\frac{1}{3}\) (or width to length \(\frac{3}{1}\)).

Step2: Convert units and check each option

• Option A: \(16\,\text{cm} \times 36\,\text{cm}\). Ratio \(\frac{16}{36}=\frac{4}{9}

eq\frac{1}{3}\).

• Option B: \(50\,\text{cm} \times 100\,\text{cm}\). Ratio \(\frac{50}{100}=\frac{1}{2}

eq\frac{1}{3}\).

• Option C: \(1\,\text{m} \times 2\,\text{m}\). Ratio \(\frac{1}{2}

eq\frac{1}{3}\).

• Option D: \(0.5\,\text{m} \times 1.5\,\text{m}\). Ratio \(\frac{0.5}{1.5}=\frac{1}{3}\), which matches the original ratio.

Answer:

D. \(0.5\,\text{m} \times 1.5\,\text{m}\)