Calculate Rectangle Perimeter: Area = 10, Width = 5 Units

Rectangle Perimeter with Given Area

If the area of the rectangle shown below is equal to 10.

Calculate the perimeter of the rectangle.

101010555222AAABBBDDDCCC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the perimeter of the rectangle
00:03 The perimeter of the rectangle equals the sum of its sides
00:10 Opposite sides are equal in a rectangle
00:16 Insert the relevant values into the formula according to the given data and proceed to solve for the perimeter
00:20 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

If the area of the rectangle shown below is equal to 10.

Calculate the perimeter of the rectangle.

101010555222AAABBBDDDCCC

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=5 AB=CD=5

AC=BD=2 AC=BD=2

Now we can calculate the perimeter of the rectangle by adding all the sides together:

2+5+2+5=4+10=14 2+5+2+5=4+10=14

3

Final Answer

14

Key Points to Remember

Essential concepts to master this topic
  • Area Formula: Use Area = length × width to find missing dimension
  • Calculation: If Area = 10 and width = 5, then length = 10 ÷ 5 = 2
  • Perimeter Check: Add all four sides: 2 + 5 + 2 + 5 = 14 ✓

Common Mistakes

Avoid these frequent errors
  • Using area value as perimeter
    Don't think that Area = 10 means Perimeter = 10! Area measures the space inside the rectangle, while perimeter measures the distance around it. Always find the missing dimension first, then add all four sides together.

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

How do I find the length when I only know area and width?

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Use the area formula backwards! Since Area = length × width, you can find length by dividing: length = Area ÷ width. In this problem: length = 10 ÷ 5 = 2.

Why do I add the sides twice in the perimeter formula?

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A rectangle has four sides, but opposite sides are equal! So you have two lengths and two widths. The formula Perimeter = 2 × length + 2 × width accounts for all four sides.

What's the difference between area and perimeter?

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Area measures the space inside the rectangle (square units), while perimeter measures the distance around the rectangle (linear units). They're completely different measurements!

Can I use the formula P = 2(l + w) instead?

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Yes! P=2(l+w) P = 2(l + w) is the same as adding all four sides. With length = 2 and width = 5: P=2(2+5)=2(7)=14 P = 2(2 + 5) = 2(7) = 14

How do I know which measurement is length and which is width?

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In rectangles, it doesn't matter which you call length or width! The longer side is typically called length, but for calculations, you can use either dimension as long as you're consistent.

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