Rectangle Perimeter Application: Feet of Fencing Required

Welcome to an application problem involving perimeter. Here we’re given that Wally wants to add a fence to the back of his house to make some room for his children to play safely. Looking at the diagram below. Here’s Wally’s house and were given the length of the fence here is five feet, this length is ten feet and this length is three feet. He began measuring his yard but got distracted and forgot to finish measuring before he went to the store. If he remembered that the back wall of his house is fifteen yards long. Does he have enough information to buy the fencing he needs? If so, how many feet should he by? So he remembered that this length, the back wall of this house has a length of fifteen yards. He does have enough information to determine how much fencing he needs however, notice how these lengths are measured in feet, and this length is given in yards. We need to convert this length to feet, and because one yard is equal to three feet, fifteen yards is equal to fifteen times three feet, or forty-five feet. If you want to be more formal about this conversion, we can write fifteen yards as a fraction with the denominator of one. And then multiply by a unit fraction to convert the units from yards to feet. Because one yard is equal to three feet we can form two unit fractions. Either one yard over three feet, or three feet over one yard. Because we want the units of yards to simplify out, we would put the units of yards in the denominator and feet in the numerator. And the conversion is one yard equals three feet. Notice in this form, units of yards simplifies out leaving us with fifteen times three feet, which does give us forty-five feet. Okay, now going back to the diagram, we need to find this length here in feet to determine how much fencing he needs. Well looking at the information here, we have five feet plus forty-five feet, plus three feet and therefore, this length is fifty-three feet. And we also know that if this length is ten feet, the opposite side would have to be ten feet. Now we can determine how many feet of fencing he should purchase. The fence will go from here to here, along the back down here and back to the house. So if we let f equal the amount of fencing in feet, we can say that f is equal to, let’s start here. So five plus ten, plus fifty-three, plus ten, plus three, the units would be feet. Let’s go ahead and find this sum though. F is equal to five plus ten is fifteen, fifteen plus fifty-three is equal to sixty-eight, plus ten is seventy-eight, plus three is eighty-one. And therefore, the amount of fencing Wally needs is eighty-one feet. So Wally should buy eighty-one feet of fencing. I hope you found this helpful.

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