Question

a scale drawing for a restaurant is shown below. in the drawing, 3 cm represents 4 m. assuming the dining hall is rectangular, find the area of the real dining hall. area of the real dining hall: m²

Explanation:

Step1: Find the real - life length of the dining hall

Given that \(3\) cm represents \(4\) m. The length of the dining hall in the drawing is \(9\) cm.
Let \(x\) be the real - life length. Using the proportion \(\frac{3}{4}=\frac{9}{x}\) (since the scale is consistent). Cross - multiply: \(3x = 4\times9\), so \(x=\frac{4\times9}{3}=12\) m.

Step2: Find the real - life width of the dining hall

The width of the dining hall in the drawing is \(3\) cm. Let \(y\) be the real - life width. Using the proportion \(\frac{3}{4}=\frac{3}{y}\). Cross - multiply: \(3y = 4\times3\), so \(y = 4\) m.

Step3: Calculate the area of the rectangular dining hall

The area formula for a rectangle is \(A=\text{length}\times\text{width}\). Substitute the real - life length \(l = 12\) m and width \(w = 4\) m. So \(A=12\times4 = 48\) \(m^{2}\).

Answer:

\(48\)