A scale drawing for a restaurant is shown below. In the drawing , 2 cm represents 5 m.
Assuming the dining hall is rectangular, find the area of the real dining hall
To find the area of the real dining hall, we first need to calculate the dimensions of the dining hall in the scale drawing.
Let the length of the dining hall in the drawing be L cm and the width be W cm.
From the scale, we have:
2 cm represents 5 m
So, if the length in the drawing is L cm, then the real length of the dining hall is:
Real length = L cm * 5 m/2 cm = 5/2L m
Similarly, if the width in the drawing is W cm, then the real width of the dining hall is:
Real width = W cm * 5 m/2 cm = 5/2W m
The area of the real dining hall is:
Area = Real length * Real width
Area = (5/2L) * (5/2W)
Area = 25/4 * (L * W) m^2
Therefore, the area of the real dining hall is 25/4 times the area of the dining hall in the drawing.