Q:

# 1. If 1 cm represents 10 m, what are the actual measurements of the gym includingthe closet?2. What are the actual measurements of the closet?3. If 1 cm represents 12 m, what are the actual measurements of the gym includingthe closet?4. What is the area of the gym?

Accepted Solution

A:
Answer:1.  50 meters by 40 meters2.  20 meters by 10 meters3.  60 meters by 48 meters4. Drawing Gym Area = 18 sq. cm. and  Actual Gym Area = 2592 sq. m.Step-by-step explanation:1.The drawing length of the GYM+CLOSET area is:5 cm by 4 cmSince 1 cm represents 10 m in real life, we can say the real life dimensions are:5cm * 10 = 50 meters4 cm * 10 = 40 metersTHe actual measurements of gym (including closet):50 meters by 40 meters2.The drawing measurement of the closet would be:2 cm length given and 1 cm width givenSince we know 1 cm represents 10 meters in real life, the actual measurements would be:1cm * 10 = 10 meters2 cm * 10 = 20 metersThe actual dimensions of closet:20 meters by 10 meters3.Gym + Closet area is still 5cm by 4cm in the drawing.Now, the scale changes. The new scale is:1cm = 12 metersSo,5cm * 12 = 60 meters4 cm * 12 = 48 metersThe actual measurement of Gym and Closet (new scale):60 meters by 48 meters4.First, let find the area of the gym. This will be total area - closet areaWe know area of rectangular figure is Length * WidthSO,Total Area = 5 * 4 = 20Closet Area = 2 * 1 = 2Thus,Gym Area = 20 - 2 = 18Gym Area = 18 sq. cm.In real life (1cm = 12 m -- new scale), Gym Area would be:Gym Area = $$18cm^2*\frac{12m}{1cm}*\frac{12m}{1cm}=18*12*12m^2=2592m^2$$Actual Gym Area = 2592 sq. m.