Find Side Length x+4 in a Square with Area 36

Q: Why do I get two answers when taking the square root?

When you solve $ (x+4)^2 = 36 $, taking the square root gives both positive and negative solutions: $ x+4 = ±6 $. This is mathematically correct, but you must check which solutions are valid for the problem!

Q: What does the constraint x > -4 actually mean?

The constraint $ x > -4 $ ensures the side length $ x+4 $ is positive. Since lengths can't be negative in geometry, this constraint eliminates impossible solutions.

Q: How do I know which solution to pick?

Check both solutions against the given constraints! For $ x = 2 $: side = 6 cm ✓. For $ x = -10 $: side = -6 cm ✗ (impossible length).

Q: Can I solve this without using the constraint?

You could solve the equation, but you'd get the wrong answer! The constraint isn't just decoration - it's essential for determining which mathematical solution makes sense in the real-world context.

Square Area Problems with Algebraic Expressions

In front of you is a square.

The expressions listed next to the sides describe their length.

( $x>-4$ length measurements in cm).

Since the area of the square is 36.

Find the lengths of the sides of the square.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the lengths of the sides of the square

00:03 We'll use the formula for calculating the area of a square (side squared)

00:09 We'll substitute appropriate values according to the given data and solve for X

00:14 We'll take the square root to eliminate the square

00:17 When taking a square root, remember we get 2 solutions

00:20 One positive and one negative

00:23 Let's isolate the unknown and find the solution for each possibility

00:29 This is one solution

00:33 This solution doesn't fit the given domain

00:37 Let's find the second solution using the same method

00:41 This is the solution for X

00:43 Now let's substitute this solution in the expression for the side, and solve to find the side

00:51 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

In front of you is a square.

The expressions listed next to the sides describe their length.

( $x>-4$ length measurements in cm).

Since the area of the square is 36.

Find the lengths of the sides of the square.

Step-by-step solution

To solve for the side length of the square, we follow these steps:

Step 1: Given each side of the square as $x+4$ cm, use the area formula for a square: $\text{Area} = (\text{side length})^2$ .
Step 2: Since the area is 36 cm $^2$ , set up the equation:

$(x+4)^2 = 36$ .

Step 3: Solve for $x+4$ :

Taking the square root of both sides,

$x+4 = 6$ or $x+4 = -6$ .

Step 4: Solve each equation for $x$ :

From $x+4 = 6$ , we get $x = 2$ .
From $x+4 = -6$ , we get $x = -10$ .

Step 5: Apply the condition $x > -4$ :

Only $x = 2$ satisfies the condition $x > -4$ .

Step 6: Calculate the side length using $x = 2$ :

Side length = $x+4 = 2+4 = 6$ cm.

Therefore, the length of the sides of the square is $6$ cm.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Square Area Formula: Area equals side length squared: $(x+4)^2 = 36$
Square Root Method: Take square root of both sides: $x+4 = ±6$
Constraint Check: Verify $x > -4$ condition: only $x = 2$ works ✓

Common Mistakes

Avoid these frequent errors

Forgetting to check domain constraints
Don't accept x = -10 just because it solves the equation = negative side length! This violates the given condition x > -4 and creates an impossible geometric situation. Always check that your solution satisfies all given constraints and makes physical sense.

Practice Quiz

Test your knowledge with interactive questions

Find the value of the parameter x.

$$ 2x^2-7x+5=0 $$

FAQ

Everything you need to know about this question

Why do I get two answers when taking the square root?

When you solve $(x+4)^2 = 36$ , taking the square root gives both positive and negative solutions: $x+4 = ±6$ . This is mathematically correct, but you must check which solutions are valid for the problem!

What does the constraint x > -4 actually mean?

The constraint $x > -4$ ensures the side length $x+4$ is positive. Since lengths can't be negative in geometry, this constraint eliminates impossible solutions.

How do I know which solution to pick?

Check both solutions against the given constraints! For $x = 2$ : side = 6 cm ✓. For $x = -10$ : side = -6 cm ✗ (impossible length).

Can I solve this without using the constraint?

You could solve the equation, but you'd get the wrong answer! The constraint isn't just decoration - it's essential for determining which mathematical solution makes sense in the real-world context.

What if I forgot to expand (x+4)²?

You don't need to expand! The most efficient method is to take the square root directly: $\sqrt{(x+4)^2} = \sqrt{36}$ , which gives you $|x+4| = 6$ .

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