TenMarks teaches you how to use scale factor concepts to solve real life problems.
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Learn Applications of Scale Factor In this video lesson, we’ll learn about scale factors. We’re given two problems. Let’s do them one by one. The first problem says rectangle A which is given below is similar to a rectangle B that we have to draw and the scale factor from rectangle A to B is 3. What are the dimensions? That’s what we need to find, the dimensions of rectangle B. Let’s do this. I’m going to take a little bit of space and try Problem 1. We are given rectangle A which is given above. I’m going to redraw it and it has one dimension as 7 centimeters which is the length and the width is 5 centimeters. That’s what’s were given. We are also given that there’s a rectangle B, we need to find the dimensions of this but the scale factor given to us is 3. So, here is what we know. What we know is the length of A = 7 centimeters. We know the width of rectangle A= 5 centimeters. That’s were given. We don’t know the length of B or the width of B but what we do know is the scale factor. What is the scale factor B? Scale factor is the length of A over the length of B which is the ratio of their corresponding sides. Corresponding side is the length or the width of A over the width of B equals the scale factor which in this case is 3. What are we given? Let’s substitute the values. We know the length of A is 7 centimeters, length of B, let’s call it L of B = width of A which is 5 centimeters over width of B equals scale factor which is 3. So now that we know this, we can take these two first and solve for length of B. So, 7 centimeters divided by the length of B equals 3. That’s what we’re given. By cross multiplying, this gives us length of B×3 which is one multiplication equals 7 centimeters. I’m going to divide both sides by 3 which gives me length of B = 7/3 centimeters. Let’s look at the second one which is the width of B. Width of B, I can determine by using this against 3. So, 5 centimeters divided by width of B equals 3 which means by cross multiplying, I get 5 centimeters = 3 × width of B. We can divide both sides by 3 again and we get 5/3 centimeters = width of B. So, what do we ultimately find out? The rectangle B has dimensions, length is 7/3 centimeters and the width is 5/3 centimeters. I can write this in decimals as well if you want. This will be slightly greater than 2, so this will be equals 2. 3×2 is 6, 2.33 centimeters and this will be 1.66 centimeters. Let’s look at the second problem which says two rectangles A and B are similar. We’re given two rectangles that are similar. Dimensions of rectangle A are 5 centimeters by 4 centimeters. Find the scale factor, that’s what we need to find from rectangle A to rectangle B, if the area of the rectangle B is 80 cm2. Let’s write down what we know. In the second problem we are given that there’s a rectangle A which measures 5 centimeters by 4 centimeters. This is rectangle A. We are also given a rectangle B where the area of rectangle B is 80 cm2. We need to find the scale factor. That’s what we need to determine. What is the area of rectangle A? Area of rectangle A is length × width which is 5 × 4, 5 centimeters × 4 centimeters = 20 cm2. So now, what do we know? From this, what we know is area of rectangle A = 20 cm2 and we know the area of rectangle B is given to us as 80 cm2. If area of rectangle A is 20 and the area of rectangle B is 80 then the (scale factor)2 = area B/area A because this is in cm2 and this is in cm2. What are we given? Well, area B is 80, area A is 20, centimeter on both sides. 80/20 = 4. So, square of the scale factor is 4. (Scale factor)2 = 4 or a scale factor = under root of 4 which is 2. So, the ultimate answer we were looking for, the scale factor is 2 and where we got that is we looked at the area of rectangle A, we looked at the area of rectangle B. Area of rectangle A, we computed, area of rectangle B was given to us. If we have the areas of two rectangles, the scale factor times itself or (scale factor)2 = ratio of the two. Ratio of the t