Calculate Rectangle Perimeter: Area = 78, Dimensions 13 × 6

Q: What's the difference between area and perimeter?

Area is the space inside the rectangle (length × width = 78). Perimeter is the distance around the outside (add all four sides = 38).

Q: Why do I add 13 + 6 + 13 + 6 instead of just 13 + 6?

A rectangle has four sides! Two sides are 13 units long and two sides are 6 units long. You need to walk around the entire rectangle to find the perimeter.

Q: Can I use the formula P = 2l + 2w instead?

Absolutely! $ P = 2(13) + 2(6) = 26 + 12 = 38 $. This formula is just a shortcut for adding all four sides.

Q: What if the problem only gave me the area?

You'd need both dimensions to find perimeter. Just knowing area = 78 isn't enough because many different rectangles can have area 78 (like 1×78, 2×39, 3×26, etc.).

Rectangle Perimeter with Given Dimensions

If the area of a rectangle is 78.

Calculate the perimeter of the rectangle.

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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

00:09 Opposite sides are equal in a rectangle

00:16 Substitute the relevant values into the formula according to the given data and solve for the perimeter

00:20 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

If the area of a rectangle is 78.

Calculate the perimeter of the rectangle.

Step-by-step solution

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

$AB=CD=13$

$AC=BD=6$

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

$6+13+6+13=12+26=38$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Rectangle perimeter equals 2 times length plus 2 times width
Technique: Add opposite sides: $13 + 6 + 13 + 6 = 38$
Check: Verify dimensions multiply to given area: $13 \times 6 = 78$ ✓

Common Mistakes

Avoid these frequent errors

Using area formula instead of perimeter formula
Don't multiply length times width (13 × 6 = 78) when asked for perimeter! That gives you area, not the distance around the rectangle. Always add all four sides: 13 + 6 + 13 + 6 = 38.

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?

FAQ

Everything you need to know about this question

What's the difference between area and perimeter?

Area is the space inside the rectangle (length × width = 78). Perimeter is the distance around the outside (add all four sides = 38).

Why do I add 13 + 6 + 13 + 6 instead of just 13 + 6?

A rectangle has four sides! Two sides are 13 units long and two sides are 6 units long. You need to walk around the entire rectangle to find the perimeter.

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

Absolutely! $P = 2(13) + 2(6) = 26 + 12 = 38$ . This formula is just a shortcut for adding all four sides.

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

It doesn't matter for perimeter! Whether you call 13 the length and 6 the width (or vice versa), you'll get the same perimeter of 38.

What if the problem only gave me the area?

You'd need both dimensions to find perimeter. Just knowing area = 78 isn't enough because many different rectangles can have area 78 (like 1×78, 2×39, 3×26, etc.).

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