1. if 1 cm represents 10 m, what are the actual measurements of the gym including
the 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 including
the closet?
4. what is the area of the gym?

1.  50 meters by 40 meters

2.  20 meters by 10 meters

3.  60 meters by 48 meters

4. 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 cm

Since 1 cm represents 10 m in real life, we can say the real life dimensions are:

5cm * 10 = 50 meters

4 cm * 10 = 40 meters

THe actual measurements of gym (including closet):

50 meters by 40 meters

2.

The drawing measurement of the closet would be:

2 cm length given and 1 cm width given

Since we know 1 cm represents 10 meters in real life, the actual measurements would be:

1cm * 10 = 10 meters

2 cm * 10 = 20 meters

The actual dimensions of closet:

20 meters by 10 meters

3.

Gym + Closet area is still 5cm by 4cm in the drawing.

Now, the scale changes. The new scale is:

1cm = 12 meters

So,

5cm * 12 = 60 meters

4 cm * 12 = 48 meters

The actual measurement of Gym and Closet (new scale):

60 meters by 48 meters

4.

First, let find the area of the gym. This will be total area - closet area

We know area of rectangular figure is Length * Width

SO,

Total Area = 5 * 4 = 20

Closet Area = 2 * 1 = 2

Thus,

Gym Area = 20 - 2 = 18

Gym Area = 18 sq. cm.

In real life (1cm = 12 m -- new scale), Gym Area would be:

Gym Area =

Actual Gym Area = 2592 sq. m.

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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