What is Finding a Missing Side Given Perimeter?

S1-SA3-0914

Grade Level:

Class 5

Geometry, Engineering, Computing, AI, Algebra

Definition

What is it?

Finding a missing side given perimeter means using the total boundary length (perimeter) of a shape and the lengths of its known sides to calculate the length of an unknown side. It's like knowing the total distance you walked around a park and how far you walked on three sides, then figuring out the distance of the fourth side.

Simple Example

Quick Example

Imagine you have a rectangular cricket ground. You know the total boundary (perimeter) is 400 meters. You also know the length is 120 meters and the width is 80 meters. If you only knew the perimeter and one length, you could find the other length.

Worked Example

Step-by-Step

Let's say a triangular field has a perimeter of 100 meters. Two of its sides measure 30 meters and 40 meters. We need to find the length of the third side.

Step 1: Understand the formula for perimeter of a triangle: Perimeter = Side 1 + Side 2 + Side 3.
---Step 2: Write down the known values: Perimeter = 100 m, Side 1 = 30 m, Side 2 = 40 m. Let the missing side be 'x'.
---Step 3: Substitute the known values into the formula: 100 = 30 + 40 + x.
---Step 4: Add the known side lengths: 30 + 40 = 70.
---Step 5: Rewrite the equation: 100 = 70 + x.
---Step 6: To find 'x', subtract 70 from both sides: x = 100 - 70.
---Step 7: Calculate the result: x = 30 meters.

So, the length of the missing side is 30 meters.

Why It Matters

This skill is super useful in many fields! Architects use it to plan building layouts, ensuring walls fit perfectly within a given boundary. In engineering, it helps design components like gears or circuits where total length is fixed. Even computer programmers use similar logic for game development or robotics to manage object dimensions efficiently.

Common Mistakes

MISTAKE: Forgetting to subtract all known sides from the perimeter. | CORRECTION: Always sum up all the given side lengths first, then subtract that total from the perimeter.

MISTAKE: Confusing perimeter with area. | CORRECTION: Remember, perimeter is the total distance around the outside of a shape, while area is the space inside the shape.

MISTAKE: Applying the formula for a square (Perimeter = 4 * side) to a rectangle or triangle. | CORRECTION: Use the correct perimeter formula for the specific shape you are working with (e.g., Triangle: sum of 3 sides; Rectangle: 2 * (length + width)).

Practice Questions

Try It Yourself

QUESTION: A square photo frame has a perimeter of 48 cm. What is the length of one side? | ANSWER: 12 cm

QUESTION: A rectangular school ground has a perimeter of 300 meters. If its length is 90 meters, what is its width? | ANSWER: 60 meters

QUESTION: A farmer wants to fence a plot of land that is shaped like a pentagon (5 sides). The perimeter of the plot is 250 meters. Four of the sides measure 45m, 50m, 55m, and 40m. How long is the fifth side? | ANSWER: 60 meters

MCQ

Quick Quiz

A table top is shaped like a triangle. Its perimeter is 180 cm. If two sides are 60 cm and 70 cm, what is the length of the third side?

50 cm

40 cm

60 cm

70 cm

The Correct Answer Is:

The perimeter of a triangle is the sum of its three sides. So, 60 cm + 70 cm + missing side = 180 cm. This means 130 cm + missing side = 180 cm. Therefore, the missing side is 180 cm - 130 cm = 50 cm.

Real World Connection

In the Real World

Think about a tailor making a dress. They might have a certain length of decorative lace (perimeter) they want to put around a specific part of the dress. If they know the lengths of some edges, they can calculate how much lace is needed for the remaining edge, ensuring no waste. Or, in construction, when building a fence around a house, knowing the total fence material available (perimeter) helps calculate the length of the last section.

Key Vocabulary

Key Terms

PERIMETER: The total distance around the outside of a 2D shape | MISSING SIDE: An unknown side length of a shape | RECTANGLE: A four-sided shape with four right angles and opposite sides equal | TRIANGLE: A three-sided polygon | FORMULA: A mathematical rule expressed in symbols

What's Next

What to Learn Next

Great job understanding how to find a missing side! Next, you can explore 'Area of Different Shapes'. This will build on your knowledge of dimensions and help you understand the space inside shapes, not just their boundaries. Keep up the good work!