Learn about Application of Similarity Figures Let’s learn how to apply similar figures in real life. So let’s give these problems some thought. Matt swims in a pool that is similar to an Olympic-size pool. so I'm going to start documenting what we already know. So what we know is Matt’s pool is similar to an Olympic size pool. This is given to us. Matt’s pool is 40 meters long. So, Matt’s pool length equals 40 meters and 7 meters wide. Matt’s pool width is 7 meters. We are given if the length of the Olympic size pool is 80 meters. So, Olympic pool length equals 80 meters. We need to find the width of the Olympic size pool. Width is what we need to determine. Now we have all the facts written down. We are given that these two figures are similar. If they are similar then the ratio of their corresponding sides are proportional or equivalent. This is the key fact. So, if that’s the case let’s change the color of our pen and look at what we know, ratio of the corresponding sides. Well, let’s look at Matt’s pool. So Matt’s pool’s length/Matt’s pool width. That’s the ratio of their corresponding sides. Of the corresponding side will be the Olympic length/the Olympic pool width. What we’re told is the ratio of their corresponding sides is proportional. We know that. That means a length of/the width of the Matt’s pool is the same as length/width of the Olympic pool and we talk about the ratios. So let’s substitute the values that we know. Matt’s pool’s length is 40 meters over width is 7 meters equals Olympic pool length is 80 meters, Olympic pool width we don’t know. So, let’s call this W. So, that’s what we know and we know these two ratios are equivalent then we can cross multiply. If we cross multiply, we get 40 meters times W which the width equals 80 meters x 7 meters. Let’s divide both sides left and right by 40. So, we get width equals 80 meters x 7 meters/40 meters. Taking a little bit more space, this means that the width equals 80x7 is 560/40 is 14 meters. So the width of the pool which is the Olympic size pool is 14 meters. That’s the answer we were looking for. Quickly recapping what we’ve learned, if we are given word problems we can write down what we know and then remember that the ratio of corresponding sides are always proportional or equivalent if the figures are similar which means we can draw the ratios out, use cross multiply to get the missing dimension which is the width of the Olympic size pool that is 14 meters.