Rectangle Perimeter Problem: Finding the Distance Around a 21-Square-Unit Shape

Q: Why do I need to add all four sides when opposite sides are equal?

Even though opposite sides are equal, perimeter means the total distance around the entire rectangle. You're walking around the whole shape, so you count every side: length + width + length + width.

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

Absolutely! $ P = 2(l + w) = 2(7 + 3) = 2(10) = 20 $. This formula is just a shortcut for adding all four sides, since you have two lengths and two widths.

Q: What if I'm given different dimensions but the same area?

Different rectangles can have the same area but different perimeters. For example, a 1×21 rectangle also has area 21, but its perimeter is $ 2(1 + 21) = 44 $!

Q: How can I check if my area calculation is right?

Multiply length × width: $ 7 \times 3 = 21 $. This should match the given area. If it doesn't, double-check that you're reading the dimensions correctly from the diagram.

Rectangle Perimeter with Given Area Dimensions

If the area of the rectangle is 21.

Determine the perimeter of the rectangle.

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Understand the problem

If the area of the rectangle is 21.

Determine 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:

$AB=CD=7$

$AC=BD=3$

Now let's add all the sides together to calculate the perimeter:

$3+7+3+7=6+14=20$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Rule: Opposite sides are equal in length always
Technique: Add all four sides: 7 + 3 + 7 + 3
Check: Verify area equals length × width: 7 × 3 = 21 ✓

Common Mistakes

Avoid these frequent errors

Only adding two sides instead of all four
Don't calculate 7 + 3 = 10 and call it the perimeter! This only gives you two adjacent sides, not the distance around. Perimeter means the total distance around all four sides. Always add all sides: 7 + 3 + 7 + 3 = 20.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why do I need to add all four sides when opposite sides are equal?

Even though opposite sides are equal, perimeter means the total distance around the entire rectangle. You're walking around the whole shape, so you count every side: length + width + length + width.

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

Absolutely! $P = 2(l + w) = 2(7 + 3) = 2(10) = 20$ . This formula is just a shortcut for adding all four sides, since you have two lengths and two widths.

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

It doesn't matter! In this problem, you can call 7 the length and 3 the width, or vice versa. The perimeter will be the same either way: 20 units.

What if I'm given different dimensions but the same area?

Different rectangles can have the same area but different perimeters. For example, a 1×21 rectangle also has area 21, but its perimeter is $2(1 + 21) = 44$ !

How can I check if my area calculation is right?

Multiply length × width: $7 \times 3 = 21$ . This should match the given area. If it doesn't, double-check that you're reading the dimensions correctly from the diagram.

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