Finding Length of Unknown Sides
Basics on the topic Finding Length of Unknown Sides
Finding the Length of Unknown Sides
Freddie and Zuri are trying to build a new climbing wall but they are a bit stuck with the instructions as some of the side lengths are missing. In this video we will learn how to find the length of the missing side.
The first piece of climbing wall is a rectangular shape. Freddie and Zuri know the perimeter and the lengths of two sides but want to find the missing lengths. To find the length of missing sides on a rectangle;
 Add together known side lengths
 Subtract total from perimeter
 As the shape is a rectangle with unknown opposite sides, divide the answer by two
The second piece of climbing wall is an irregular shape with only one missing side length. Freddie and Zuri know the perimeter but need to find the missing side length.
 If it is a shape with one unknown side, add together known sides
 Subtract total from perimeter.
Always check your work by adding all the sides together to see if it matches the perimeter. 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 centimetres or metres, we can 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. Next, subtract the total of the known side lengths from the PERIMETER. TWENTYSIX minus SIX equals TWENTY. Since rectangles have opposite sides equal in length, we divide TWENTY by TWO, to find EACH 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 twentysix. 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? 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 of 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 TWENTYTWO. What is the second step? Subtract the total of the known side lengths from the PERIMETER, which is twentyfive units. TWENTYFIVE minus TWENTYTWO 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 of the sides together to get twentyfive. 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. Then, subtract the total of the known side lengths from the PERIMETER. 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 of 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!"
Finding Length of Unknown Sides exercise

How can we find the missing lengths of the sides?
HintsLook 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 First, add together the known side lengths. 8 + 8 = 16.
 Then, subtract the total of the known side lengths from the perimeter. 24  16 = 8.
 This shape is a rectangle so opposite sides are equal. We therefore divide 8 by 2 to get 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?
HintsWhat 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?
2 + 2 = 4
18  4 = 14
14 ÷ 2 = ? This is the answer.
SolutionThe 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?
HintsIf the shape is only missing one side length, subtract the total of the given lengths from the perimeter. This is your answer.
If the shape is a rectangle, first subtract the two known lengths from the perimeter. The total left will be the amount for two sides, so divide this by 2.
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.
 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?
HintsStart 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.
SolutionVan door
 The missing side length was 4 units.
 5 + 5 + 4 + 1 + 1 = 16
 20  16 = 4
 The missing side lengths were 5 units each.
 6 + 6 = 12
 22  12 = 10
 10÷ 2 = 5
 The missing side length was 4 units.
 9 + 6 + 3 + 6 + 2 = 26
 30  26 = 4
 The missing side length was 2 units.
 2 + 2 + 2 + 2 + 2 = 10
 12  10 = 2
 The missing side length was 3 units.
 2 + 2 + 2 + 3 = 9
 12  9 = 3
 The missing side lengths were 2 units each.
 3 + 3 = 6
 10  6 = 4
 4÷ 2 = 2

What is the missing side length?
HintsAdd up the given side lengths and subtract the answer from the perimeter.
5 + 2 + 2 + 3 + 3 = 15
20  15 = ?
SolutionThe 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?
HintsWork 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?
SolutionThe missing side lengths from the rectangular piece were 9 units each.
 6 + 6 = 12
 30  12 = 18
 18÷ 2 = 9
 6 + 2 + 2 + 2 + 4 + 2 + 5 + 7 = 30
 33  30 = 3
 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.