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Finding Length of Unknown Sides

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Finding the Length of Unknown Sides

To find the length of missing sides on a rectangle;

  • Add together known side lengths
  • Subtract total from perimeter
  • If the shape is a rectangle with unknown opposite sides, divide the answer by two
  • If it is a shape with 1 unknown side, the answer is the length
  • Check your work by adding all the sides together

Below you will find a worksheet on finding the length of unknown sides.

Transcript Finding Length of Unknown Sides

It looks like Zuri and Freddie have found something! "We have to build this climbing wall!" "Yes, but there are side lengths missing, Zuri!" Let's help Zuri and Freddie find the length of unknown sides. When finding missing side lengths, we can use the given perimeter to help us. Perimeter is the total distance around the outside of a shape. If no unit of measurement is given, like feet or yards, we use the term units to measure perimeter. You may be asked to find missing side lengths of rectangles, where opposite side lengths are unknown. Before we help Zuri and Freddie, let's see how to find missing side lengths. Here we have a rectangle, with two unknown side lengths. Rectangles have two opposite sides equal in length. In order to find the unknown lengths, first, add together the known side lengths. Three plus three equals six. Second, subtract the total of the known side lengths from the perimeter. Twenty-six minus six equals twenty. Third, since rectangles have opposite sides equal in length, we divide twenty by two, to find find missing side length. Twenty divided by two equals ten. The missing side lengths of the rectangle are ten units each. Finally, check the answer by adding together all sides to make sure it is the same as the perimeter. Three plus three plus ten plus ten equals twenty-six. Let's help Zuri and Freddie find the unknown side lengths on the blueprint now! Here is the frame of the climbing wall. We can see it is a rectangle, with two unknown side lengths. What is the first step? First, add the known side lengths. Six plus six equals twelve. What is the second step? Second, subtract the total of the known side lengths from the perimeter, which is twenty units. Twenty minus twelve equals eight. What is the third step? Since opposite sides of a rectangle are equal in length, we divide eight by two. Eight divided by two equals four. The missing side lengths of the frame are four units each. Finally, we check our work by adding all the sides together to get twenty units. Now let's help Zuri and Freddie find the missing side length of the front of the climbing wall! This time, it is an irregular polygon shape with only one unknown side length. Since only one side length is unknown, we will only need to do the first two steps to solve this one but we will still check our work! What is the first step? First, add the known side lengths. Six plus six plus eight plus two equals twenty-two. What is the second step? Second, subtract the total of the known side lengths from the perimeter, which is twenty-five units. Twenty-five minus twenty-two equals three. Since there is only one unknown side length, this is our answer. The missing side length is three units. Finally, we check our work by adding all the sides together to get twenty-five. While Zuri and Freddie finish building the climbing wall let's review! Remember, you can find unknown side lengths using a given perimeter. First, add together the known side lengths. Second, subtract the total of the known side lengths from the perimeter. Third, if the shape is a rectangle and opposite sides are unknown, divide the answer by two, or if the shape has only one unknown side, this is the unknown length! Finally, check your work by adding all the sides together and check against the perimeter. "Freddie, I can't do this, I'm so scared!" "Me too Zuri... just don't look down!"

1 comment
1 comment
  1. what I`d like to know is how to convert the area to a perimeter! and the other way around!

    From Ethan, 5 months ago

Finding Length of Unknown Sides exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Finding Length of Unknown Sides.
  • How can we find the missing lengths of the sides?

    Hints

    Look at the perimeter. Remember, this is the total length of all sides added together.

    What shape is this piece of climbing wall? What does that tell us?

    What should we do at the end to make sure we have the correct answer?

    Solution
    1. First, add together the known side lengths. 8 + 8 = 16.
    2. Then, subtract the total of the known side lengths from the perimeter. 24 - 16 = 8.
    3. This shape is a rectangle so opposite sides are equal. We therefore divide 8 by 2 to get 4.
    4. Check your work by adding all of the sides together. 8 + 8 + 4 + 4 = 24.
  • What are the missing lengths of the sides on this piece?

    Hints

    What is the total of the known side lengths? Work this out and then subtract it from the perimeter.

    After subtracting, divide what is left by two as this shape is a rectangle.

    How can you check your answer?

    Solution

    The missing side lengths are 7 units each.

    • 2 + 2 = 4.
    • If we subtract 4 from 18, we get 14.
    • We then divide 14 by 2, to get 7.
    • Therefore the missing side lengths are 7 units each.
  • What are the missing side lengths of these pieces?

    Hints

    Add up the given side lengths first.

    If the shape is only missing one side length, subtract the total of the given lengths from the perimeter. This is your answer.

    If your shape is a rectangle:

    • Subtract the total of the given lengths from the perimeter.
    • Divide this by two.
    • This is your answer.

    Solution
    • The first shape had two missing side lengths of 6 units each.
    • The second shape had two missing side lengths of 2 units each.
    • The third shape had a missing side length of 3 units.
    • The fourth shape had a missing side length of 4 units.
    _______________________________________________________

    The first and second shapes are rectangles.

    • First we need to add the missing side lengths e.g. 4 + 4 = 8.
    • We then subtract this from the perimeter e.g. 20 - 8 = 12.
    • We then divide this by two e.g. 12 ÷ 2 = 6.
    • This is the answer: the two missing side lengths are 6 units each.
    The other two shapes just had one missing side length.
    • First we add up the given side lengths e.g. 6 + 2 + 3 + 1 + 3 = 15.
    • We then subtract this from the perimeter e.g. 18 - 15 = 3.
    • This is the answer: the missing side length is 3 units.
  • Can you find the missing side lengths of these items?

    Hints

    Start by adding up all of the known side lengths.

    Subtract the total of the known side lengths from the perimeter.

    What you are left with is the answer if you are looking for one missing side length.

    If the shape is a rectangle and you are looking for two missing side lengths, you need to divide by two.

    Solution

    Van door

    • The missing side length was 4 units.
    • 5 + 5 + 4 + 1 + 1 = 16
    • 20 - 16 = 4
    Pizza box
    • The missing side lengths were 5 units each.
    • 6 + 6 = 12
    • 22 - 12 = 10
    • 10÷ 2 = 5
    Desk top
    • The missing side length was 4 units.
    • 9 + 6 + 3 + 6 + 2 = 26
    • 30 - 26 = 4
    Mirror
    • The missing side length was 2 units.
    • 2 + 2 + 2 + 2 + 2 = 10
    • 12 - 10 = 2
    Clock
    • The missing side length was 3 units.
    • 2 + 2 + 2 + 3 = 9
    • 12 - 9 = 3
    Book
    • The missing side lengths were 2 units each.
    • 3 + 3 = 6
    • 10 - 6 = 4
    • 4÷ 2 = 2

  • What is the missing side length?

    Hints

    Add up the given side lengths and subtract the answer from the perimeter.

    5 + 2 + 2 + 3 + 3 = 15

    20 - 15 = ?

    Solution

    The missing side length is 5 units.

    5 + 2 + 2 + 3 + 3 = 15. 20 - 15 = 5

    We can check our answer too: 5 + 5 + 2 + 2 + 3 + 3 = 20

  • What is the perimeter of the climbing wall?

    Hints

    Work out the individual missing side lengths using the method you have been using.

    • Add up the given side lengths.
    • Subtract this from the perimeter.
    • If the shape is a rectangle, divide this number by two.

    Remember, two sides will be stuck together. The red lines show where they will be stuck together. Do you need to count these when working out the total perimeter?

    Solution

    The missing side lengths from the rectangular piece were 9 units each.

    • 6 + 6 = 12
    • 30 - 12 = 18
    • 18÷ 2 = 9
    This missing side length from the other piece was 3 units.
    • 6 + 2 + 2 + 2 + 4 + 2 + 5 + 7 = 30
    • 33 - 30 = 3
    To find the total perimeter:
    • The two sides of 6 units that are next to each other would have been stuck together, so we don't count these in the final perimeter.
    • So we can then add 6 + 9 + 2 + 2 + 2 + 4 + 3 + 2 + 5 + 7 + 9 = 51 units.
    • We could also add 6 + 6 = 12 and add 30 + 33 = 63. We can then subtract 12 from 63 to get 51.