 Hello and welcome to the session. In this session we will discuss a question which says that the dimensions of a window are 2.65 feet by 1.75 feet. A scale drawing of window has dimensions 3 by 4 inches by 1 by 2 inches. Find scale and scale factor. Now before starting the solution of this question we should know some results. And the first result is scale drawing is a proportional two dimensional drawing of an object and scale is equal to drawing dimension upon actual dimension. Now a scale can be written without units when units are same in joint and in actual and a scale without units is called scale factor. Now these results will work out as a key idea for solving out the given question. Now let's start with the solution of the given question. Now we have given a window and its scale drawing and here the dimensions of window are given as 2.65 feet by 1.75 feet and dimensions of its scale drawing are given as 3 by 4 inches by 1 by 2 inches. Now we know that scale drawing is a proportional two dimensional drawing of an object. This means these two figures are similar. Now first of all we have to find the scale. Now from the key idea we know that scale is equal to drawing dimension upon actual dimension so as the scale is equal to drawing dimension upon actual dimension. Now here in these two figures you can see that actual width of this window is 1.75 feet whereas the width of this window in this drawing is 1 by 2 inches. So scale will be equal to drawing dimension which is 1 by 2 inches upon actual dimension which is 1.75 feet. Similarly we can find the scale by comparing the length that is the length in actual and length in drawing. Now the actual length is 2.65 feet and length in scale drawing is 3 by 4 inches. So scale is equal to drawing dimension which is 3 by 4 inches upon actual dimension which is 2.625 feet. Now when we convert this scale in same units then both of them will give us same results. Now we have to find scale factor and we know that a scale without units is called a scale factor. So first of all let us write this scale without units. Now we know that 1 foot is equal to 12 inches so 1.75 feet will be equal to 1.75 into 12 inches which is equal to 21 inches. Now 1.72 inches upon 1.75 feet will be equal to 1 by 2 inches upon now 1.75 feet is equal to 21 inches further this is equal to 1 by 2 upon 21 which is equal to 1 upon 2 into 21. Now 2 into 21 is 42. Now here this scale is written without units so here scale factor is equal to 1 by 42 or we can write it as 1 is to 42. Now if we will write this scale without units then again we will get the same result. So let us take this scale which is 3 by 4 inches upon 2.625 feet further this is equal to 3 by 4 inches upon now converting feet into inches this will be 2.625 into 12 inches further this is equal to 3 by 4 inches upon 31.5 inches which can be written as 3 by 4 upon 31.5 which is equal to 3 upon 4 into 31.5 and this is equal to 3 upon 126 now 3 into 42 is 126 so this is equal to 1 upon 42. So again we are getting scale factor is equal to 1 is to 42. Now we know that these 2 figures are similar and we know that in 2 similar figures corresponding sides are proportional. So from the figures n is equal to upon ABQR upon VC. So this is the solution of the given question and that is all for this session. Hope you all have enjoyed the session.