TenMarks teaches you how to find the measures of scale drawing using proportions.
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Find the Measurement So in this problem, Sylvia measured a house and its lot and made a scale drawing. She used the scale 1in=9ft. The backyard deck is 54 feet long in real life. How long is the deck in the drawing? All right, so in this problem we need to find the length in the drawing. Set up a ratio in the form of a fraction. So, we need to set up a ratio to find the length of the deck in the drawing. So, the ratio is going to be in fraction form. So, when we talk about scale, scale is the ratio of length on a drawing to the actual length, so the length of the drawing or on the drawing to the actual length. So, the scale in this problem is 1in=9ft or 1 inch to 9 feet. So, it’s the length in the drawing to the actual length. So, our scale is 1in/9ft. Now, the actual length of the deck is 54 feet long. We need to write in equivalent fraction with 54 feet as the denominator so, what need to do is write an equivalent fraction with 54 in the denominator. And that will help us find, because the length of the deck is 54 feet long, so the numerator of the fraction gives the length of the model. So, we know that 9*6 gives us 54. So, that means that we need to multiply the denominator and the numerator by six. So therefore, we’re going to take our one inch and multiply that by six right from our scale. And then we’re going to take our nine feet. So, 9ft*6 and that will be 6/54. So in the drawing, the deck is six inches long. Now, let’s move onto our second problem. Here we have Julie. And Julie measured a city park and made a scale drawing. The scale she used was 1cm=5m. In the drawing, the soccer field is 11 centimeters wide, that is the width of the actual field? So in this problem, we need to find the width of the actual field. So, we’re going to set up a ratio in fraction form. So, we know that our scale is 1cm=5m. So, if we put this in a fraction, it will be 1cm/5m. Now, we know that the length on the scale is 11 centimeters. So, we need to write an equivalent fraction with 11 centimeters as the numerator. So, we’re going to write 11 centimeters, we’ve to set up an equivalent fraction with 11 centimeters as the numerator. So, what we need to do is we’re going to multiply the numerator and the denominator by 11 because I know 11*1 would give me 11 in my numerator. So, I’m going to take my one centimeter and my five meters and I’m going to multiply by 11 and that will give me 11/55. So, the actual field is 55 meters wide. Remember that when we talk about scale, scale gives a ratio that compares the measurements on a drawing or model. So, the ratio of length to the drawing to the actual length, it compares the measurements on the drawing or model to the measurements of the real object. When we talk about the ratio on a map, we’re comparing the distance to the actual distance. So, we compare the map distance to the actual distance. And the actual distance must remain the same, that is the two ratios must be in proportion.