Rectangle with Area 70: Calculate the Perimeter Using Given Dimensions

Rectangle Perimeter with Given Dimensions

If the area of a rectangle is equal to 70.

Calculate the perimeter of the rectangle.

707070101010777AAABBBDDDCCC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's determine the perimeter of the rectangle.
00:10 The perimeter is the total length around the rectangle. Add up all the sides.
00:15 Remember, in a rectangle, opposite sides are equal.
00:22 Now, plug in the given values, and calculate the perimeter.
00:26 Great job! That's how we find the perimeter.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

If the area of a rectangle is equal to 70.

Calculate the perimeter of the rectangle.

707070101010777AAABBBDDDCCC

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

AC=BD=7 AC=BD=7

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

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

3

Final Answer

34

Key Points to Remember

Essential concepts to master this topic
  • Formula: Perimeter = 2(length + width) for rectangles
  • Technique: Add all four sides: 10 + 7 + 10 + 7 = 34
  • Check: Opposite sides equal: length = 10, width = 7 ✓

Common Mistakes

Avoid these frequent errors
  • Using area formula instead of perimeter formula
    Don't calculate length × width = 70! That gives you the area again, not perimeter. The area is already given as 70. Always add all four sides together for perimeter: 10 + 7 + 10 + 7 = 34.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

1.51.51.5AAABBBCCCDDD9.5

FAQ

Everything you need to know about this question

Why do I add the sides instead of multiplying them?

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Perimeter means the distance around the shape, so you walk along each side and add up the distances. Area is the space inside, which uses multiplication.

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

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It doesn't matter for perimeter! Whether you call 10 the length or width, you still have two sides of 10 and two sides of 7, giving the same perimeter of 34.

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

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Absolutely! P=2(10+7)=2(17)=34 P = 2(10 + 7) = 2(17) = 34 . This is often faster than adding all four sides individually.

What if the rectangle was rotated differently?

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The perimeter stays the same! No matter how you orient the rectangle, the sides are still 10 and 7, so the perimeter is always 34.

How do I verify my perimeter is correct?

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Check that opposite sides are equal and your arithmetic is right. For this rectangle:

  • Two sides of 10: ✓
  • Two sides of 7: ✓
  • Total: 10 + 7 + 10 + 7 = 34 ✓

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