PROPORTION AND SCALE DRAWING Learning Objectives After implementing

PROPORTION AND SCALE DRAWING

§ § § Learning Objectives: After implementing this lesson students will be able to: Explaining the concept of proportion Determine proportion of two number Find a size in a map, actual measurement or scale Find the size of a photo / model or real object Calculate enlargement factor and reduction factor in scale drawing The characters building: Discipline, respect, diligence and responsibility.

PROPORTION �To be easier in comprehending proportion, see following description. v Mila has 10 books, and Ryan has 4 books. We can determine the proportion of the number of Mila’s books to the number of Ryan’s books in way follows: The number of Mila’s books : The number of Ryan’s books = 10 : 4 2 2 =5: 2 So, the proportion of the number of Mila’s books to the number of Ryan’s books is 5 : 2 or can be written

The concept of proportion: v. If a and b are two quantities which unit the same (similar) then the comparison of a and b is written: a : b or can also be written , with a and b are positive rational numbers

1. PROBLEM EXAMPLES: Express proportion in following problems! The price of bag is Rp. 80. 000, 00 and the price of shoes is Rp. 120. 000, 00 Answer: the proportion of price of bag to the price of shoes is The price of bag : the price of shoes = 80. 000 : 120. 000 40. 000 = 2 : 3 So, the proportion of price of bag to the price of shoes is 2 : 3 q

2. A rectangle has a width of 80 cm and a length of 1, 4 meters. Express proportion in this problems! q Answer: because the unit of length of rectangle isn’t similar with the unit of width’s, then we must equate the first unit. length = 1, 4 meters = 1, 4 x 100 = 140 cm The proportion of width to length rectangle is width rectangle : length rectangle = 80 : 140 20 20 = 4 : 7 So, The proportion of width to length rectangle is 4 : 7

SCALE DRAWING The figure behind is a map of the East Kalimantan Province with a scale of 1 : 8, 000. Scale 1 : 8, 000 It means that 1 cm on the map represents 8, 000 cm in the actual size. This scale is a ratio of the size on the map to the actual size. In other words 8, 000 cm in reality will be drawn on the map as 1 cm. Scale = Distance on the map : Real distance.

PROBLEM EXAMPLES Look at the map of East Kalimantan. What is the real distance between Tanjung Redeb and Tanjung Selor ! q Answer: �On the map, measure the distance between Tanjung Redeb and Tanjung Selor. The distance on the map is about 2. 7 cm. �Scale 1 : 8, 000 �The real distance = 2. 7 x 8, 000 = 21, 600, 000 1. Therefore, the distance between Tanjung Redeb and Tanjung Selor is 21, 600, 000 cm = 216 km (1 km = 100, 000 cm).

2. q On the same map, distance between Sengata and Bontang is 1, 5 cm. What is the real distance between Sengata and Bontang? Answer: �Scale 1 : 8, 000 �The real distance = 1. 5 x 8, 000 = 12, 000. Therefore, the real distance between Sengata and Bontang is 12, 000 cm = 120 km (1 km = 100, 000 cm).

3. The distance between Samarinda and Tarakan in East Kalimantan Province is 672 km. Find distance between the cities on the map with scale of 1 : 8, 000. q Answer: � Scale 1 : 8, 000 � Real distance = 672 km = 67, 200, 000 cm � Let: The distance on the map = x cm. = � Scale = distance on the map : real distance. 8, 000 x = 67, 200, 000 x= x= = 8. 4 So, the distance between Samarinda and Tarakan on

4. On another map, the distance between Surabaya and Banyuwangi is 3 cm. The real distance between those cities is 120 km. Find the scale of the map ! Answer: �Distance on the map = 3 cm �Real distance = 120 km = 12, 000 cm �Scale = Distance on the map : Real distance. = 3 : 12, 000 (simplified by dividing it by q 3) = 1 : 4, 000

Photos and Scale Models Before a car or house is constructed, usually a model of that car or house is made. Parts of the car or house have the same ratio as the corresponding parts (namely height, width, and length) of the model. = =

PROBLEM EXAMPLES: 1. The heights of a door and a window model are 9 cm and 6 cm, respectively. The real height of window is 1 m. What is the real height of the door? q Answer: � The height of the door model is 9 cm. � The height of the window model is 6 cm. � The real height of the window is 1 m = 100 � The height of the door is x cm. = = 6 x = 9. 100 6 x = 900 x = 150 So, The height of the door is 150 cm.

A car model has length 12 cm and width 4 cm. The real length of car is 6 m. What is the real width of the car? q Answer: � The lengthof the car model is 12 cm. � The width of the car model is 4 cm. � The real length of the car is 6 m = 600 cm. � The real width of the car is x cm. 2. = = 12 x = 4. 600 12 x = 2400 (simplified by dividing it by 12) x = 200 So, The real width of the car is 200 cm.

Enlargement Factor and Reduction Factor in scale drawing

Poblem Example The size of photo A is 4 x 6 and the size of photo B is 2 x 3. What is the ratio of photo A to photo B ? q Answer: � The size of photo A is 4 x 6, which means 4 cm in width and 6 cm in length. � The size of photo B is 2 x 3, which means 2 cm in width and 3 cm in length. = = v The o The and = = ratio of photo B to photo A is 1 : 2. size of photo B is as a result of the reduction of times of photo A. Coversely, the size of photo A is the enlargement of 2 times of photo B. Ø Thus, the reduction factor of photo A to photo B is Ø Meanwhile, the enlargement factor of photo B to photo A is 2.

EXERCISE 1. 2. 3. 4. State the following proportions in the simplest forms ! a) 5 kg : 4 ounces b) 60 : one full rotation c) 1 hours : 30 minutes d) 3 m : 2, 500 dm A cupboard has a height of 200 cm, a length of 100 cm and a width of 60 cm. If that cupboard is modeled with the height of 20 cm, find the length and the width of the model. A building which is seen on a television screen is 10 cm in height and 8 cm in width. If the width of building is 42 m, what is its height? A football field has a size of 75 m x 110 m. The distance from the penalty point to the goal is 11 metres. a) Make a scale drawing of that field with the scale 1 : 1, 000. b) Find the distance from the penalty point to the goal in your scaled drawing.