 Hello and welcome to the session. In this session we will discuss a question which says that an architect's drawing for a new school building shows the library as 8.4 cm long. If the scale on the drawing is 1 cm is equal to 4 meters, what is the length of the actual library? Now before starting the solution of this question we should know a result. And that is scale is equal to drawing dimension upon actual dimension and a scale can be written without units when units are same in drawing and in actual and a scale written without units is called scale factor. Now this result will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Now in this question scale is given to us also length of library in scale drawing is given to us and we have to find length of actual library. Now we have to find length of actual library. Now there are two methods by which we can solve this question. Let us discuss the method one. Now in method one we will make the use of scale. Now from the key idea we know that scale is equal to drawing dimension upon actual dimension. Now here length of library in scale drawing is 8.4 cm. Now let actual length of library be any meters. Now given scale is equal to 1 cm upon 4 meters. Also from the key idea scale is equal to drawing dimension and here drawing dimension is 8.4 cm upon n which is n meters. Therefore we have 1 cm upon 4 meters is equal to 8.4 cm upon n meters. This implies n is equal to 4 cm upon 1 cm into 4 meters which is equal to 8.4 into 4 meters which is equal to 33.6 meters. Therefore length of actual library is equal to 33.6 meters. Now let us discuss the second method of solving this question and in this method we will make the use of scale factor. Now again from the key idea we know that a scale without units is called scale factor. Now scale is given to us as 1 cm upon 4 meters. So given scale is equal to 1 cm upon 4 meters. Now let us write this scale without units. Now we know that 1 meter is equal to 100 cm. So 4 meters will be equal to 4 into 100 cm which is equal to 400 cm. So now 1 cm upon 4 meters will be equal to 1 cm upon. Now 4 meters is equal to 400 cm. Therefore this is equal to 1 upon 400 cm. So here we converted the drawing dimension and x-ray dimension in same units and hence we obtain a scale without units. So this scale without units is called scale factor. So scale factor is 1 is to 400. Now scale factor is equal to drawing dimension upon x-ray dimension. Now in case of scale factor both the drawing and x-ray dimensions are in cm. So let the actual length of library be L cm. And it is given that length of library in scale drawing is 8.4 cm. Now scale factor is equal to 8.4 cm upon L cm. Or we can write it as 8.4 upon L cm. Now this implies now we have scale factor is equal to 1 upon 400 cm. So this will be equal to 8.4 upon L cm. Which further implies L is equal to 8.4 into 400 cm. Which is equal to 3360 cm. Which is equal to 3360 upon 100 meters. Which is equal to 33.60 meters. Or simply 33.6 meters. Therefore length of actual library is equal to 33.6 meters. So we can use scale and we can use scale factor to find the length of actual library which is equal to 33.6 meters. And this is the solution of the given question. Let's work for this session. Hope you all have enjoyed this session.