Question

a scale drawing for a restaurant is shown below. in the drawing, 4 cm represents 5 m. assuming the dining hall is rectangular, find the area of the real dining hall. area of the real dining hall: m²

Explanation:

Step1: Calculate the actual length of the dining hall

Given that \(4\) cm represents \(5\) m. The length of the dining hall in the drawing is \(8\) cm.
Let \(x\) be the actual length. Set up a proportion: \(\frac{4}{5}=\frac{8}{x}\). Cross - multiply: \(4x = 5\times8\), so \(x=\frac{5\times8}{4}=10\) m.

Step2: Calculate the actual width of the dining hall

The width of the dining hall in the drawing is \(4\) cm. Let \(y\) be the actual width. Using the proportion \(\frac{4}{5}=\frac{4}{y}\). Cross - multiply: \(4y=5\times4\), so \(y = 5\) 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 actual length \(l = 10\) m and actual width \(w = 5\) m. So \(A=10\times5=50\) \(m^{2}\).

Answer:

\(50\)