Calculate Side Length: Finding Square Dimensions from Area 144

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

Because area equals side × side (or s²). To find the original side length, you need to reverse the squaring operation by taking the square root!

Q: How do I remember the difference between area and perimeter?

Area measures space inside (multiply: length × width). Perimeter measures distance around the edge (add: all four sides together).

Q: Can the side length be negative?

No! Side lengths represent distance, which is always positive. Even though $ (-12)^2 = 144 $, we only use the positive square root for geometric measurements.

Square Root Applications with Perfect Squares

A square has an area of 144.

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 side of the square

00:03 Use the formula for calculating the area of a square (side squared)

00:08 Substitute appropriate values and solve for the side

00:13 Extract the root

00:23 And this is the solution to the question

00:26 Chapter Title

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A square has an area of 144.

How long are its sides?

Step-by-step solution

Remember that the area of a square is equal to the side of the square raised to the 2nd power.

We replace the data in the formula:

$144=L^2$

Then we calculate the root:

$\sqrt{144}=L$

$L=12$

Final Answer

$12$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of square equals side length squared (A = s²)
Technique: Take square root of area: $\sqrt{144} = 12$
Check: Verify by squaring result: $12^2 = 144$ ✓

Common Mistakes

Avoid these frequent errors

Confusing area with perimeter formulas
Don't divide 144 by 4 thinking it's perimeter = wrong answer of 36! Area uses multiplication (s²), not addition like perimeter (4s). Always remember area = side × side for squares.

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 take the square root of the area?

Because area equals side × side (or s²). To find the original side length, you need to reverse the squaring operation by taking the square root!

What if the area isn't a perfect square like 144?

You'll get a decimal or irrational answer. Use a calculator to find $\sqrt{150} ≈ 12.25$ , but always check your work by squaring your answer.

How do I remember the difference between area and perimeter?

Area measures space inside (multiply: length × width). Perimeter measures distance around the edge (add: all four sides together).

Can the side length be negative?

No! Side lengths represent distance, which is always positive. Even though $(-12)^2 = 144$ , we only use the positive square root for geometric measurements.

What's the easiest way to check my answer?

Square your answer and see if you get back to the original area. If $12^2 = 144$ , then 12 is correct!

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