Question

the drawing below was created using a scale of 1 cm : 2 meters. what is the actual area of the room in square meters? width = 4 cm length = 6 cm

Explanation:

Step1: Determine the scale factor

Assume the scale is \( 1 \, \text{cm} : x \, \text{meters} \). From the problem, we can infer that the scale is \( 1 \, \text{cm} : 2 \, \text{meters} \) (since it's a common scale for such problems, and likely the intended scale here as the drawing has width 4 cm and length 6 cm).

Step2: Find the actual length

The drawing length is \( 6 \, \text{cm} \). Using the scale \( 1 \, \text{cm} = 2 \, \text{m} \), the actual length \( L = 6 \times 2 = 12 \, \text{meters} \).

Step3: Find the actual width

The drawing width is \( 4 \, \text{cm} \). Using the scale, the actual width \( W = 4 \times 2 = 8 \, \text{meters} \).

Step4: Calculate the actual area

The area of a rectangle is \( A = L \times W \). Substituting the values, \( A = 12 \times 8 = 96 \, \text{square meters} \).

Answer:

The actual area of the room is \( \boxed{96} \) square meters.