Introduction to Finding Missing Lengths

Hello Year 5! Today, we are going to learn about finding missing lengths. This is an important skill in maths because it helps us solve problems involving shapes and measurements.

What does ‘missing lengths’ mean?

Sometimes, when we look at a shape or a figure, we might know some of the lengths (like the sides of a rectangle) but not all of them. We will learn how to find those missing lengths using some simple rules and calculations.

Key Rules

  1. Understanding Shapes: Different shapes have different rules. For example, a rectangle has two long sides and two short sides. The opposite sides are the same length.
  2. Using Addition and Subtraction: To find a missing length, you might need to add or subtract lengths you already know.
  3. Using Formulas: For some shapes, we can use formulas. For instance, the perimeter (the distance around a shape) of a rectangle can be found with the formula: \text{Perimeter} = 2 \times (\text{Length} + \text{Width})
  4. Checking Your Work: Once you find a missing length, check it by plugging it back into the original problem to see if it makes sense.

Tips and Tricks

  • Draw a Diagram: If you’re unsure, drawing the shape can help you see what lengths you have and what you need to find.
  • Look for Patterns: In many shapes, lengths repeat or relate to each other. Use this to your advantage!
  • Break it Down: If the problem seems complicated, break it down into smaller parts. Solve one part at a time.

Examples

Example 1: Rectangle

You have a rectangle with a length of 5 cm and a width of 3 cm. What is the perimeter?

  1. Use the formula: \text{Perimeter} = 2 \times (5 + 3)
  2. Calculate: \text{Perimeter} = 2 \times 8 = 16 \text{ cm}

Example 2: Missing Length

In a rectangle, the length is 8 cm, and the perimeter is 24 cm. What is the width?

  1. Use the formula for perimeter: 24 = 2 \times (8 + \text{Width})
  2. Divide by 2: 12 = 8 + \text{Width}
  3. Subtract 8 from both sides to find the width: \text{Width} = 12 – 8 = 4 \text{ cm}

Practice Questions

Easy Level

  1. A rectangle has a length of 6 cm and a width of 2 cm. Find the perimeter.
  2. If one side of a square is 4 cm, what is the perimeter?
  3. A triangle has sides of 3 cm, 4 cm, and a missing side. If the perimeter is 12 cm, what is the missing side?
  4. A rectangle has a length of 10 cm and a missing width. If the perimeter is 30 cm, find the width.
  5. The width of a rectangle is 5 cm. If the length is double the width, what is the length?
  6. A square has a perimeter of 24 cm. What is the length of one side?
  7. A rectangle has a length of 7 cm and a width of 3 cm. Find the length of the diagonal.
  8. If the perimeter of a rectangle is 20 cm and the length is 6 cm, find the width.
  9. A triangle has two sides measuring 5 cm and 7 cm. If the perimeter is 20 cm, what is the missing side?
  10. A square has a side length of 5 cm. What is the perimeter?

Medium Level

  1. The perimeter of a rectangle is 36 cm. If the length is 10 cm, what is the width?
  2. A triangle has sides of 5 cm, 12 cm, and a missing side. If the perimeter is 30 cm, find the missing side.
  3. A rectangle has a width of 4 cm and a perimeter of 28 cm. What is the length?
  4. Find the missing length of a rectangle if the perimeter is 40 cm and the width is 8 cm.
  5. A square has a perimeter of 32 cm. What is the area of the square?
  6. The length of a rectangle is 12 cm and the width is 6 cm. Find the length of the diagonal.
  7. A triangle has sides of 9 cm, 12 cm, and a missing side. If the perimeter is 40 cm, what is the missing side?
  8. A rectangle has a length of 15 cm and a width that is half the length. Find the width.
  9. The perimeter of a square is 48 cm. What is the area of the square?
  10. Find the missing length in a triangle with sides of 8 cm, 6 cm, and a perimeter of 30 cm.

Hard Level

  1. A rectangle has a perimeter of 50 cm. If the length is 18 cm, find the width.
  2. The perimeter of a triangle is 36 cm. If two sides are 10 cm and 12 cm, find the missing side.
  3. A rectangle has a length that is 3 times its width. If the perimeter is 48 cm, what are the dimensions of the rectangle?
  4. A square has an area of 64 cm². What is the length of one side?
  5. In a right-angled triangle, the lengths of the two shorter sides are 9 cm and 12 cm. Find the length of the hypotenuse.
  6. A rectangle has a width of 5 cm and a perimeter of 36 cm. Find the length.
  7. The perimeter of a triangle is 50 cm. If the sides are in the ratio 2:3:5, find the lengths of each side.
  8. A rectangle has a length of 14 cm and a width that is 2 cm less than the length. What is the width?
  9. If a square has a diagonal of 10 cm, what is the length of one side?
  10. A triangle has two sides measuring 7 cm and 4 cm. If the perimeter is 30 cm, find the missing side.

Answers

Easy Level Answers

  1. 16 cm
  2. 4 cm
  3. 5 cm
  4. 5 cm
  5. 10 cm
  6. 6 cm
  7. 7.6 cm (using Pythagoras)
  8. 4 cm
  9. 8 cm
  10. 20 cm

Medium Level Answers

  1. 8 cm
  2. 13 cm
  3. 10 cm
  4. 12 cm
  5. 64 cm²
  6. 13.9 cm (using Pythagoras)
  7. 19 cm
  8. 7.5 cm
  9. 144 cm²
  10. 16 cm

Hard Level Answers

  1. 7 cm
  2. 14 cm
  3. Length = 12 cm, Width = 4 cm
  4. 8 cm
  5. 15 cm
  6. 13 cm
  7. 10 cm, 15 cm, 25 cm
  8. 12 cm
  9. 7.07 cm
  10. 19 cm

Now you have a good understanding of finding missing lengths! Remember to practice these types of questions to become more confident in your skills. Happy learning!