Question

a scale drawing for a restaurant is shown below.
in the drawing, 3 cm represents 5 m.
assuming the dining hall is rectangular, find the area of the real dining hall.
area of the real dining hall: (\text{ }\text{m}^2)

Explanation:

Step1: Calculate the real - length of the dining hall

Given that \(3\) cm represents \(5\) m. For the length of the dining hall which is \(6\) cm on the drawing.
Let \(x\) be the real - length. Set up a proportion: \(\frac{3}{5}=\frac{6}{x}\). Cross - multiply gives \(3x = 5\times6\), so \(x=\frac{5\times6}{3}=10\) m.

Step2: Calculate the real - width of the dining hall

For the width of the dining hall which is \(3\) cm on the drawing. Let \(y\) be the real - width. Set up a proportion: \(\frac{3}{5}=\frac{3}{y}\). Cross - multiply gives \(3y = 5\times3\), 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 real - length \(l = 10\) m and real - width \(w = 5\) m. Then \(A=10\times5=50\) \(m^{2}\).

Answer:

\(50\)