Sarah uses a roll of border fencing that is 25 and one-fourth feet long to surround a rectangular flower bed in her garden. If the width of the flower bed is one and five-eighths feet, what is its length?
Let’s think about what we know. Sarah has a flower bed with a rectangular fence around it. The border fencing is 25 and one-fourth feet long. Mathematically, we would call this the perimeter, the distance around a 2D shape. And because a rectangle has two sets of equal sides, we add the length twice and then the width twice to find the perimeter. If the distance around Sarah’s flower bed, the perimeter of her flower bed, was 25 and one-fourth feet, we want to know what the length of the flower bed is. And we already know that the width was one and five-eighths feet.
Our first step will be to add up how much of the fence is used on the two pieces representing the width of the flower bed. This means we need to add one and five-eighths plus one and five-eighths. If we add the two fractions, they need a common denominator. Both of these fractions are out of eight. And that means we can add their numerators together. Five-eighths plus five-eighths equals ten-eighths. And one plus one equals two. But we noticed that ten-eighths is an improper fraction. We could write two and ten-eighths as two plus eight-eighths plus two-eighths. And we know that eight-eighths equals one. So we would add two plus one to get three, three and two-eighths.
We can simplify one final time. Two-eighths is the same as one-fourth. We can divide our numerator by two and our denominator by two. And that reduces two-eighths to one-fourth. This means that the width takes up three and one-fourth feet of the total fencing. If three and one-fourth of the total fencing is used on the width, we can subtract that from the amount of total fencing used. One-fourth minus one-fourth equals zero. And 25 minus three equals 22.
This means there are 22 feet left to be divided evenly between the two length sides. 22 divided by two equals 11. This means that the length of Sarah’s flower bed was 11 feet. 11 plus 11 equals 22. And one and five-eighths plus one and five-eighths equals three and one-fourth. When we add all four of these sides together, we get 25 and one-fourth feet. And so, we can say that the length of Sarah’s flower bed is 11 feet.