 Hello and welcome to the session. In this session we will discuss scale drawings, scale factor and how to reproduce scale drawings at different scale. First of all, let us learn what is a scale drawing. Now many times we make use of drawings to represent an object which is very large in size like maps of different cities. Also there are some things which we want to make, but first we make the drawing to see how they should look like. Like an architect prepares drawing of the house with dimensions on a paper before actually constructing it. Now let us illustrate it with the help of an example. Now if we have a large size carpet with length 45 feet and width 25 feet, then we can make a similar carpet on a paper with length is equal to 9 inches and width is equal to 5 inches. So here this is the actual carpet and this is the drawing of the carpet and here on the drawing 1 inch represents 5 feet. It means 1 inch on the drawing represents 5 feet in the real world. So here on the drawing 5 inches represents 25 feet and 9 inches represents 45 feet and such a drawing is called scale drawing. So a scale drawing is defined as a drawing which is a proportional 2 dimensional drawing of an object. Scale model is a proportional 3 dimensional model of an object. Now let us learn what is a scale factor. Now measurement in scale drawing and models are proportional to the measurement of an actual object. Now the scale gives ratio that compares the measurement of the drawings with actual measurements. Now here we know that 1 inch in drawing represents 5 feet in real world. That means 1 inch is the drawing dimension and 5 feet is the actual dimension. Now in ratio we can write it as 1 inch is to 5 feet. Now here the scale is equal to 1 inch upon 5 feet. Now a scale can be written without units when units are same in drawing and in actual. And a scale without units is called scale factor. Now let us write the scale without units. Now we know that 1 foot is equal to 12 inches. So 5 feet will be equal to 5 into 12 inches which is equal to 60 inches. So now this can be written as 1 inch upon 60 inches which is equal to. Now here both of them are same units. So it will be equal to 1 upon 60 or we can write it as 1 is to 60. Now here the scale is written without units. It means 1 is to 60 is the scale factor. So the scale factor is 1 is to 60. So the scale factor is equal to drawing dimension upon actual dimension. Now let us discuss an example. Now in this example it is given that a model of a space shuttle has a scale of 1 is to 48. And it is also given that the space shuttle has a wingspan of 67 feet the model's wingspan. Now here we can see that this is the actual space shuttle and this is the model of this space shuttle. Now we know that scale or scale factor is equal to drawing dimension upon actual dimension. Now here we have to find model's wingspan. It means we have to find the drawing dimension and the actual dimension is given to us. So let x be the drawing dimension. Now scale or scale factor is equal to drawing dimension which is x upon actual dimension which is 67 feet. Now here the scale is given to us as 1 is to 48. So this implies 1 is to 48 is equal to x upon 67 which further implies is equal to 67 upon 48 which is equal to 1.39. Now as x is equal to 1.39 this means wingspan of the model is 1.39 feet. And here you must note one thing that here we are given scale factor that is scale without units. So units of the dimensions of both model and actual space shuttle are same that is feet and in case if scale is given in different units that is here the scale is given as 1 centimeters is to 43 meters then units of drawing dimension will be in centimeters and units of actual dimension will be in meters. Now let us learn how to reproduce a scale drawing at different scale. Now let us discuss an example for this. In this example Julie showed you the scale drawing of her garden. If each inch of the scale drawing equals 5 feet in actual then we have to find actual dimensions of her garden and also reproduce the drawing at 3 times the current size. Now here 1 inch is equal to 5 feet. It means the scale is equal to drawing dimension which is 1 inch upon actual dimension which is 5 feet. Now let actual length of the garden be x that is x feet. Now length of the garden in drawing is 6 inches. Now the scale which is 1 inch upon 5 feet is equal to drawing dimension and in case of length the drawing dimension is 6 inches and actual dimension is x feet. Now this implies x is equal to 6 inches upon 1 inch into 5 feet. Now here this will be equal to 30 feet. Now let us find the actual width of the garden. Now width in scale drawing is 4 inches. Now let actual width be y feet. Now again from the scale factor we can find y which is equal to 20 feet. So the actual length of the garden is 30 feet and actual width is 20 feet. And now we reproduce the drawing 3 times the current size of drawing without changing the actual dimensions of the garden. So the new drawing dimensions will be equal to 3 times the original drawing dimensions. So this is the new scale drawing of the garden with length 3 into 6 inches which is equal to 18 inches and width 3 into 4 inches which is equal to 12 inches. So we have produced the garden 3 times the current size. Now we can reproduce this drawing by another method also. Now as we have to reproduce the drawing 3 times the current size of the drawing first of all let us find the new scale factor. Now in new scale drawing 3 inches is equal to 5 feet. So new scale is equal to 3 inches upon 5 feet. From this new scale we get the new scale factor as 1 upon 20. Now change in scale does not change the actual dimensions. Now actual length of the garden is 30 feet which is equal to 360 inches. Now here we have converted the length in inches because we converted scale factor in inches. Now length of garden on drawing be L. Now we know that scale factor is equal to drawing dimension which is L upon actual dimension which is 360. So L is equal to 360 upon 20 which is equal to 18 inches. Similarly we can find the width of garden on drawing which is equal to 12 inches. So from this method we have calculated the length and width of new scale drawing. And here also we will obtain the new scale drawing of the garden. Now we can find area of scale drawings by using this formula. That is the square of scale factor is equal to drawing area upon actual area. Now in this example which we have discussed earlier area of wrong garden is length into breadth as it is a rectangular garden. So on calculating this will be equal to 216 square inches. And here the scale factor is 1 upon 20. So putting these values in this formula this will be 1 upon 20 whole square is equal to drawing area by just 216 square inches upon actual area. So on calculating actual area will be equal to 216 into 400 which is equal to 86,400 square inches. So in this way we can find area of scale drawings by using this formula. So in this session we have learnt about scale drawings and scale factor. And this completes our session. Hope you all have enjoyed the session.