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CCSS.Math:

sally is an architect who creates a blueprint of a rectangular dining room the area of the actual dining room is the area of the actual dining room is 1,600 times larger than the area of the dining room on the blueprint the length of the dining room on the blueprint is three inches what is the length of the actual dining room in feet so there's a couple of really interesting things going on here they give us the dimensions on the blueprint in inches we want the actual length and feet and then they tell us that the area of the actual dining room is 1,600 times larger so they're not saying that the scale of the blueprint is at 116 hundredths it's going to be something less than that and let's think about what that scale is going to be and so let's just let's just practice just think about some different scales let's say I have something let's say my let's say that my this is my blueprint and this is the actual reality of the dining room that we're thinking about now if and my blueprint is let's just say one by one just just for the sake of sake of argument now if this was a one by one a square and we increased the dimensions we increase the dimensions by a factor of by a factor of two so we increased it by a factor of two so it's a two by two square what's the what's the area are going to be well this area is going to be for this area is one this area is four so you notice that if we increase by a factor of two it increase our area by a factor of four or another way of saying if we increase our each of our dimensions by a factor of two we're going to increase our area by a factor four if instead we increased our are each of our dimensions by a factor of three by a factor of three this would be a three by three square and we would increase our area by a factor by a factor of nine so notice whatever factor we're increasing the area by it's going to be the factor that we're increasing the dimensions by squared so let's just think about it that way so they're telling us that we're increasing the area by 1,600 times so actually let me just clean this thing up a little bit so one way we could imagine it if our drawing if our drawn drawing did have an area of one which we can't assume but we could for the sake of just figuring out how much we have to what the scale of the drawing is so let me clear all of this here let me clear that so the area of of the actual dining room is 1600 times larger and so if this if the if the drawing had an area of 1 then the area of the actual dining room would be 1600 so what would I have to multiply each of the dimensions by to get a area factor of 1600 well if I multiply this dimension by 40 and this dimension by 40 we see 40 times 40 is 1600 you might say hey Sal how did you figure out 40 well the 16 is a big clue we know that 4 times 4 is equal to 16 and so if you gave a zero to each of these fours if you made it 40 times 40 then that is going to be 1600 so this information right over here tells us that the scale factor of the dimensions of the hood of the the lengths I should say that that scale factor is 40 that would result in a scale factor for the area of 1600 so that's a good starting point now let's go to the actual dining room on the blueprint so the actual dining room of the blueprint doesn't have these dimensions we just use that to figure out the scaling factor the actual dining room on the blueprint has a length of 3 inches so maybe it looks something like this they don't give us any of the other dimensions so we could even imagine a 3 inch by we could by 2 inch 1 inch whatever we want we could even three inch by three inch three inch by three and square they only care about the length now let's multiply both of these by a factor of 40 and we only care about the length here they actually say what's the length of the actual dining room so let's multiply it and obviously this is not drawn to scale let's multiply this times a factor of 40 times a factor of 40 so three times 40 is 120 three times 40 is 120 and this of course is what we're referring to as the length now you might be tempted to say okay we're done this will be 120 but remember this is 120 this is 120 inches 120 inches so what is 120 inches in terms of feet well one foot one foot is equal to 12 twelve inches if you were to multiply both of these times ten we know that 10 feet 10 feet is equal to 120 inches or another way you could have thought about it you have 120 inches divided by 12 feet divided by 12 inches per foot is going to give you 10 so 120 divided by 120 inches let me write it this way 120 inches divided by 12 inches per foot is going to give you 10 10 feet so that's the actual length of the dining room and feet