Question

a scale drawing for an apartment is shown below. in the drawing, 2 cm represents 3 m. assuming the bedroom is rectangular, find the area of the real bedroom. area of the real bedroom: m²

Explanation:

Step1: Find the actual length

Given \(2\) cm represents \(3\) m. The length of the bedroom in the drawing is \(4\) cm.
Let \(x\) be the actual length. Using proportion \(\frac{2}{3}=\frac{4}{x}\), cross - multiply: \(2x = 3\times4\), so \(x=\frac{3\times4}{2}=6\) m.

Step2: Find the actual width

The width of the bedroom in the drawing is \(6\) cm. Let \(y\) be the actual width. Using proportion \(\frac{2}{3}=\frac{6}{y}\), cross - multiply: \(2y=3\times6\), so \(y = 9\) m.

Step3: Calculate the area

The area of a rectangle \(A=\text{length}\times\text{width}\). Substitute length \(x = 6\) m and width \(y = 9\) m. \(A=6\times9 = 54\) \(m^{2}\).

Answer:

\(54\)