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How Do You Find the Length of a Rectangle if You Know its Width and Area?

The area of a rectangle with a width of five feet is 35 square feet. What is the length of the rectangle?

Summary

  1. The area, A, of the rectangle is 35 square feet
  2. The width of the rectangle is 5 feet
  3. The length, L, of the rectangle is what we're trying to find
  4. The area of a rectangle is equal to its length times its width
  5. The length of the rectangle is 7 feet
  6. Plugging our answer into the original equation shows that our answer of 7 feet was correct

Notes

    1. 'A' is a variable representing the area of the rectangle, which is 35 square feet
    1. 'W' is a variable representing the width of the rectangle, which is 5 feet
    1. 'L' is a variable representing the length of the rectangle, which is what we're trying to find
    1. 'A' is a variable representing the area of the rectangle, which is 35 square feet
    2. 'W' is a variable representing the width of the rectangle, which is 5 feet
    3. 'L' is a variable representing the length of the rectangle, which is what we're trying to find
    1. Since we're talking about a rectangle's area, knowing the equation might help us find the length
    1. Our three variables are 'A', 'W', and 'L'
    1. The equation for the area of a rectangle uses all three of our variables!
    2. 'A' is a variable representing the area of the rectangle, which is 35 square feet
    3. 'W' is a variable representing the width of the rectangle, which is 5 feet
    4. 'L' is a variable representing the length of the rectangle, which is what we're trying to find
    1. These were our given values
    2. 'A' is a variable representing the area of the rectangle, which is 35 square feet
    3. 'W' is a variable representing the width of the rectangle, which is 5 feet
    1. Here, we substituted 'A' with '35' and 'W' with '5'
    2. 'L' is a variable representing the length of the rectangle, which is what we're trying to find
    1. 'L' is a variable representing the length of the rectangle, which is what we're trying to find
    1. 'L' is a variable representing the length of the rectangle, which is what we're trying to find
    1. Division is the opposite of multiplication, so each '5' on the right side cancels out and we are left with 'L'
    2. 'L' is a variable representing the length of the rectangle, which is what we're trying to find
    1. We divided by '5' on the left, as well
    2. 35/5 = 7
    3. 'L' is a variable representing the length of the rectangle, which is what we're trying to find
    1. Try your best not to forget about the units in the problem!
    2. 'L' is a variable representing the length of the rectangle, which is what we're trying to find
    1. The length of the rectangle is 7 feet
    2. Try your best not to forget about the units in the problem!
    3. 'L' is a variable representing the length of the rectangle, which is what we're trying to find
    1. 'L = 7 ft' was our answer
    2. 'L' is a variable representing the length of the rectangle, which is what we're trying to find
    1. 'L = 7 ft' was our answer
    2. 'L' is a variable representing the length of the rectangle, which is what we're trying to find
    1. Here, we put in our given values for 'A' and 'W', and substituted 'L' with '7', our answer
    2. We have '35' on the left side of the equation
    3. We have '7 • 5' on the right side of the equation
    1. So '7 • 5' does equal '35', so we get '35' on both sides of the equation
    1. Since we had a true statement of '35 = 35', we know we did everything correctly