Calculate X in the Parallelogram: Step-by-Step to Find Height BE

Q: Why can't x be -9 if it satisfies the equation?

While $x = -9$ mathematically satisfies $x^2 = 81$, it would give us a base of -4 and height of -14. Geometric shapes cannot have negative dimensions!

Q: How do I recognize the difference of squares pattern?

Look for the form $(a+b)(a-b)$. This always equals $a^2 - b^2$. In our case, $(x+5)(x-5) = x^2 - 5^2 = x^2 - 25$.

Q: What if I expand the multiplication instead?

You can expand $(x+5)(x-5)$ using FOIL: $x^2 - 5x + 5x - 25 = x^2 - 25$. Both methods work, but recognizing the pattern is faster!

Q: How do I check my final answer?

Substitute $x = 9$ back: base = $9 + 5 = 14$, height = $9 - 5 = 4$. Area = $14 \times 4 = 56$ ✓

Q: What if the area was a different number?

The same process applies! Set up $(x+5)(x-5) = \text{new area}$, expand to $x^2 - 25 = \text{new area}$, then solve for $x^2$ and take the positive square root.

Quadratic Equations with Difference of Squares

The area of the parallelogram below is 56.

BE is its height.

Calculate x.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find the value of X.

00:09 We have a parallelogram, where opposite sides are equal.

00:18 Now, the formula for the area of a parallelogram is side times height.

00:26 Let's plug in the side values based on the information given.

00:34 Next, we'll use the area provided and solve for X.

00:45 We'll expand the brackets using multiplication formulas.

01:00 First, calculate 5 squared. What's 5 times 5?

01:09 Now, let's get X by itself in the equation.

01:20 Finally, find the root to discover the possible values of X.

01:25 And that's how we solve for X in this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The area of the parallelogram below is 56.

BE is its height.

Calculate x.

Step-by-step solution

To solve this problem, we'll calculate $x$ using the provided expressions for the base and height of the parallelogram.

Given the area of the parallelogram:

$A = (\text{base}) \times (\text{height})$

In our case, the base is $x + 5$ , and the height is $x - 5$ . Therefore, we have:

$(x + 5)(x - 5) = 56$

Recognizing this as a difference of squares, we write:

$x^2 - 25 = 56$

Add 25 to both sides to isolate $x^2$ :

$x^2 = 81$

Take the square root of both sides:

$x = \pm 9$

Since both dimensions of a parallelogram must be positive in practical applications, we take $x = 9$ .

Therefore, the correct solution is $x = 9$ .

Final Answer

$9$

Key Points to Remember

Essential concepts to master this topic

Area Formula: Parallelogram area equals base times height
Technique: Recognize $(x+5)(x-5) = x^2 - 25$ pattern
Check: Verify dimensions are positive: base = 14, height = 4 ✓

Common Mistakes

Avoid these frequent errors

Accepting negative solutions without considering context
Don't keep x = -9 just because it satisfies the equation = negative dimensions! A parallelogram can't have negative length or height. Always check that your answer makes sense in the real-world context.

Practice Quiz

Test your knowledge with interactive questions

Calculate the area of the parallelogram according to the data in the diagram.

FAQ

Everything you need to know about this question

Why can't x be -9 if it satisfies the equation?

While $x = -9$ mathematically satisfies $x^2 = 81$ , it would give us a base of -4 and height of -14. Geometric shapes cannot have negative dimensions!

How do I recognize the difference of squares pattern?

Look for the form $(a+b)(a-b)$ . This always equals $a^2 - b^2$ . In our case, $(x+5)(x-5) = x^2 - 5^2 = x^2 - 25$ .

What if I expand the multiplication instead?

You can expand $(x+5)(x-5)$ using FOIL: $x^2 - 5x + 5x - 25 = x^2 - 25$ . Both methods work, but recognizing the pattern is faster!

How do I check my final answer?

Substitute $x = 9$ back: base = $9 + 5 = 14$ , height = $9 - 5 = 4$ . Area = $14 \times 4 = 56$ ✓

What if the area was a different number?

The same process applies! Set up $(x+5)(x-5) = \text{new area}$ , expand to $x^2 - 25 = \text{new area}$ , then solve for $x^2$ and take the positive square root.

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Calculate X in the Parallelogram: Step-by-Step to Find Height BE

Quadratic Equations with Difference of Squares

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't x be -9 if it satisfies the equation?

How do I recognize the difference of squares pattern?

What if I expand the multiplication instead?

How do I check my final answer?

What if the area was a different number?

🌟 Unlock Your Math Potential

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