Finding Length of Unknown Sides — Let's Practice!

Finding Length of Unknown Sides — Let's Practice! exercise

• What are the missing side lengths?

  Hints

  Add up all of the given side lengths.

  Subtract the answer from the total perimeter.

  Solution

  1. 6 + 2 + 2 + 3 + 5 = 18; 22 - 18 = 4. The missing length is 4 units.
  2. 2 + 8 + 7 + 2 + 6 = 25; 30 - 25 = 5. The missing length is 5 units.
  3. 3 + 2 + 4 + 6 + 2 + 1 + 10 = 28; 34 - 28 = 6. The missing length is 6 units.
  4. 10 + 2 + 6 + 3 + 4 = 25; 30 - 25 = 5. The missing length is 5 units.

• Can you find the missing lengths?

  Hints

  Remember, opposite sides are equal in length on a rectangle.

  Add the two given side lengths and subtract that from the perimeter.

  Once you have done that, divide what is left by 2 to find one of the missing side lengths.

  Solution

  Grassy area

  • 6 + 6 = 12
  • 32 - 12 = 20
  • 20 $\div$ 2 = 10
  • Each missing side length is 10 m

  Bark area

  • 5 + 5 = 10
  • 18 - 10 = 8
  • 8 $\div$ 2 = 4
  • Each missing side length is 4 m.

• What are the missing side lengths?

  Hints

  Don't forget, the perimeter for all of these shapes is 22 units.

  Remember, opposite sides are equal on a rectangle.

  If you are finding the missing side of a rectangle:

  • Add the sides already given.
  • Subtract this from the total perimeter.
  • Divide the answer by two.

  If you are finding the missing side of a different shape:

  • Add the sides already given.
  • Subtract this from the total perimeter.
  • What is left is the missing side length.

  Solution

  For the first shape:

  • 7 + 7 = 14
  • 22 - 14 = 8
  • 8 $\div$ 2 = 4

  For the second shape:

  • 6 + 4 + 5 + 1 + 1 = 17
  • 22 - 17 = 5

  For the third shape:

  • 2 + 2 = 4
  • 22 - 4 = 18
  • 18 $\div$ 2 = 9

  For the fourth shape:

  • 2 + 4 + 3 + 2 + 5 = 16
  • 22 - 16 = 6

• What are the missing side lengths of the floor plan?

  Hints

  Both of the rooms are rectangles. What do you know about the side lengths of a rectangle?

  To find the missing side length of room A, first add 4 + 4 and then subtract this from 24.

  Next, divide the answer by 2.

  Can you follow these steps to find the missing side lengths of room B?

  Here is the floor plan partially filled in. To find the remaining missing side lengths, add 5 + 5 then subtract it from 24 before dividing the answer by 2.

  Solution

  Room A

  • 4 + 4 = 8
  • 24 - 8 = 16
  • 16 $\div$ 2 = 8
  • The missing length is 8 units.

  Room B

  • It is a rectangle, so even though there is only one 5 given, we know that the opposite side is also 5.
  • 5 + 5 = 10
  • 24 - 10 = 14
  • 14 $\div$ 2 = 7
  • The missing lengths are 7 units each.

• Find the missing side length.

  Hints

  Add up all of the given side lengths first.

  Subtract this from the total perimeter.

  6 + 2 + 2 + 4 + 8 = 22

  28 - 22 = ?

  Solution

  The missing length was 6 units.

  • 6 + 2 + 2 + 4 + 8 = 22
  • 28 - 22 = 6

• Find the missing values.

  Hints

  You could start by finding the missing side lengths in shape A or C.

  Once you have found the missing side length in shape C, you will be able to find the perimeter of shape B.

  Remember, a rectangle's opposite sides are equal.

  Solution

  Shape A

  • We are given a length of 4 and we know the other part of that side is 5, so we add 4 + 5 to make 9.
  • This means the opposite side is also 9.
  • We can then add 9 + 9 = 18 and subtract 18 from the perimeter, 26.
  • 26 - 18 = 8
  • 8 $\div$ 2 = 4
  • The other missing side lengths are 4 units.

  Shape C

  • 8 + 6 + 3 + 4 + 4 = 25
  • 28 - 25 = 3

  Shape B

  • Now we know the missing side length of shape C is 3 units, we can add 2 + 3 + 3 = 8.
  • We then know the opposite side is 8 units.
  • We can then add 8 + 5 + 8 + 5 = 26.
  • The perimeter of shape B is 26 units.