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

A parallelogram has a length equal to 6 cm and a height equal to 4.5 cm.

Calculate the area of the parallelogram.

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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