Calculate the Perimeter: 10 by 7 Rectangle Problem

Rectangle Perimeter with Given Dimensions

Look at the rectangle below:

AAABBBCCCDDD107

Calculate its perimeter.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the perimeter of the rectangle
00:03 Opposite sides in a rectangle are equal
00:07 The perimeter of the rectangle equals the sum of its sides
00:12 Let's solve each 2 factors separately and then sum them
00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the rectangle below:

AAABBBCCCDDD107

Calculate its perimeter.

2

Step-by-step solution

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

AB=CD=10 AB=CD=10

BC=AD=7 BC=AD=7

Now let's add all the sides together to find the perimeter of the rectangle:

10+7+10+7=20+14=34 10+7+10+7=20+14=34

3

Final Answer

34

Key Points to Remember

Essential concepts to master this topic
  • Rule: Rectangle perimeter equals twice the sum of length and width
  • Technique: Use formula P = 2(l + w) = 2(10 + 7) = 34
  • Check: Add all four sides: 10 + 7 + 10 + 7 = 34 ✓

Common Mistakes

Avoid these frequent errors
  • Using area formula instead of perimeter formula
    Don't multiply length × width (10 × 7 = 70) when finding perimeter! This gives you the area, not the distance around the shape. Always add all four sides or use P = 2(length + width) for perimeter.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?
666444AAABBBCCCDDD

FAQ

Everything you need to know about this question

What's the difference between perimeter and area?

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Perimeter is the distance around the outside of a shape (measured in units like cm). Area is the space inside a shape (measured in square units like cm²). For this rectangle, perimeter = 34 units, area = 70 square units.

Do I need to use the perimeter formula P = 2(l + w)?

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Not necessarily! You can either add all four sides (10 + 7 + 10 + 7) or use the formula P = 2(10 + 7). Both methods give the same answer: 34.

Why are opposite sides equal in a rectangle?

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By definition, a rectangle has four right angles and opposite sides that are parallel and equal. So the top and bottom sides are both 10 units, and the left and right sides are both 7 units.

What if I got 68 as my answer?

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You likely doubled the perimeter by mistake! The correct calculation is 2(10 + 7) = 2(17) = 34, not 2 × 2 × (10 + 7). Remember: only multiply by 2 once.

How can I remember the perimeter formula?

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Think of it as "going around twice" - you walk the length once, the width once, then the length again, and the width again. So it's 2 times (length + width).

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