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.

Explanation:

Step1: Find the real - 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 the real - length be $l$. We set up a proportion: $\frac{3}{4}=\frac{9}{l}$. Cross - multiplying gives $3l = 4\times9$, so $l=\frac{4\times9}{3}=12$ m.

Step2: Find the real - width of the dining hall

The width of the dining hall in the drawing is 3 cm. Let the real - width be $w$. Using the proportion $\frac{3}{4}=\frac{3}{w}$, cross - multiplying gives $3w = 4\times3$, so $w = 4$ m.

Step3: Calculate the area of the dining hall

The area of a rectangle is $A=l\times w$. Substituting $l = 12$ m and $w = 4$ m, we get $A=12\times4 = 48$ m².

Answer:

48 m²