# 5.1.1 Length Measurements

[ The foot measurement is thought to be derived from the length of a man’s foot with shoes! (If your bare foot is a foot long, you have pretty big feet). It was first defined in law by Edward I of England in 1305. Most likely, the relationship among feet, yards, and miles were made to fit existing units. These units are also defined in terms of the metric system, so for example, 1 yard is equal to 0.9144 meters. ] The common units used for measurement of length in the U.S. are inches (abbreviated in), feet (abbreviated ft), yards (abbreviated yd), and miles (abbreviated mi). Unlike the SI, there is not an easy or constant relationship among these units. In short, there are 12 inches in one foot, 3 feet in one yard, and 1760 yards, or 5280 ft, in one mile. Whoa! That’s a lot of feet. [ Perimeter and area will be discussed in greater detail in Unit 10. ] We measure items such as height, perimeter, and area using these common units. Perimeter is the total distance around an object. Area measures the size of the surface of an object.

Let’s suppose at your physical this year, your height was measured as 67 inches. How tall are you in feet and inches? First, we see how many times 12 can divide into 67, because there are 12 inches in 1 foot: . We found that there are 5 feet in 67 inches, with 7 inches left over. So, you are 5 feet 7 inches tall. This is often written 5’7” in shorthand notation.

Here’s another example. If you have a photograph that measures 8 inches by 10 inches, what is the perimeter, in feet and inches? The top and bottom of the photo have the same measurement, 8 inches. Similarly, the left side and right side share a measurement of 10 inches. Therefore, the perimeter, or the length of the border of the picture, is . Since , this means that 36 inches is the same as 3 feet. Thus, the perimeter of the picture is 3 feet.

## Activity: Length

For each of the following scenarios, use the appropriate operation and unit to determine the answer.

(a) A three-year-old girl measures 34 inches in height. Over her lifetime, she grows another 34 inches. Fully grown, how tall is she in feet and inches? ### Discussion

Try drawing pictures to help visualize each situation—you don’t need to be an artist! (a) inches

(The calculation could also be carried out using addition: inches.)

Because , this means 68 inches is the same as 5 feet and 8 inches. Thus, the woman is 5’8”, which is rather tall for a woman.

(b) A rectangular garden measures 12 feet by 18 feet. What is the perimeter of the garden in feet? In yards? ### Discussion

Make sure you know what each word means. For example, “perimeter” is a measurement of the border, or edges, of a structure. (b) Because the garden is rectangular, this means that the opposite sides have the same length. To determine the perimeter, we could just add up the sides of the garden: feet.

Alternatively, we could double each side:

. Since there are 3 feet in 1 yard, the number of yards is . Thus, the perimeter of the garden is 20 yards.

(c) During a road trip with your friends you drive 187 miles through Pennsylvania and then 225 miles in Kentucky. How many miles did you drive in total? How many feet is this?

(c) The total distance driven is .

To determine the number of feet, we need to remember that each mile contains 5,280 feet. Thus, the total distance can also be expressed as . (d) A football field measures 120 yards in length. How many yards long are four football fields if they are arranged end-to-end?  