Find Side Length of a Square: Area 25 in Similar Squares Problem

Q: Why do I need to take the square root of the area?

Because area of a square is side × side = side². To find the side length, you need to reverse this operation by taking the square root of the area.

Q: How do I know if 25 is a perfect square?

Think of multiplication facts: 5 × 5 = 25, so 25 is a perfect square. Other perfect squares include 1, 4, 9, 16, 36, 49, etc.

Q: How can I double-check my answer?

Square your answer: 5² = 25 ✓Make sure it matches the given areaCheck that your answer is positive (lengths can't be negative)

Square Area Calculations with Similar Figures

The two squares above are similar.

If the area of the small square is 25, then how long are its sides?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the length of the small square's side

00:03 Let's mark each square with numbers 1,2

00:07 Let's use the formula for calculating square area (side squared)

00:14 Let's mark the square's side as X

00:18 Let's substitute in the area formula and solve for X

00:23 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The two squares above are similar.

If the area of the small square is 25, then how long are its sides?

Step-by-step solution

The area of the large square is:
$10^2=100$

The area of the small square is 25.

$\frac{100}{25}=4$

The square root of 4 is equal to 2.

We will call X the length of the side:

$\frac{10}{x}=2$

$2x=10$

$x=5$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: For squares, area equals side length squared
Technique: If area = 25, then side = √25 = 5
Check: Verify that 5 × 5 = 25 matches given area ✓

Common Mistakes

Avoid these frequent errors

Confusing area with side length
Don't use the area (25) as the side length directly = completely wrong answer! Area is side squared, not the side itself. Always take the square root of the area to find the side length.

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

What is the area of the square?

FAQ

Everything you need to know about this question

Why do I need to take the square root of the area?

Because area of a square is side × side = side². To find the side length, you need to reverse this operation by taking the square root of the area.

What if the area isn't a perfect square?

You can still find the side length! Use a calculator to find the square root, or leave your answer in radical form like $\sqrt{18}$ .

How do I know if 25 is a perfect square?

Think of multiplication facts: 5 × 5 = 25, so 25 is a perfect square. Other perfect squares include 1, 4, 9, 16, 36, 49, etc.

Does it matter that the squares are similar?

For this specific question, no! We only need the area of the small square (25) to find its side length. The similarity tells us the squares have the same shape but different sizes.

How can I double-check my answer?

Square your answer: 5² = 25 ✓
Make sure it matches the given area
Check that your answer is positive (lengths can't be negative)

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