Calculate Rectangle Area: Finding Area When Length is 13X and Width is 2X

Q: Why do I multiply the variables x × x to get x²?

When you multiply like variables, you add their exponents. Since x has an implied exponent of 1, we get: $ x^1 \times x^1 = x^{1+1} = x^2 $

Q: What's the difference between area and perimeter?

Area measures the space inside (multiply dimensions), while perimeter measures the distance around (add all sides). For this rectangle: Area = $ 26x^2 $, Perimeter = $ 2(2x + 13x) = 30x $

Q: How do I multiply 2x and 13x step by step?

Break it into parts: coefficients and variablesMultiply numbers: 2 × 13 = 26Multiply variables: x × x = x²Combine: $ 26x^2 $

Q: Can the area ever be negative with algebraic expressions?

In real geometry, area is always positive. However, when working with algebraic expressions like $ 26x^2 $, the sign depends on the value of x. Since x² is always positive for real numbers, this area will always be positive when x ≠ 0.

Q: What if I forgot to include the x² and just wrote 26?

Always keep track of your variables! The area formula gives you $ 26x^2 $, not just 26. The x² tells you how the area changes as x changes - it's crucial information!

Rectangle Area with Algebraic Expressions

Look at the rectangle ABCD below.

AD = 2X

DC= 13X

Calculate the area of the rectangle in terms of x.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Express the area of the rectangle using X

00:03 The formula for calculating rectangle area is side(AD) times side(DC)

00:21 Let's substitute appropriate values according to the given data and calculate

00:32 Between each number and unknown there is multiplication

00:37 Therefore we can multiply number with number and unknown with unknown

00:44 Now we have an organized expression

00:51 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the rectangle ABCD below.

AD = 2X

DC= 13X

Calculate the area of the rectangle in terms of x.

Step-by-step solution

The problem requires finding the area of rectangle $ABCD$ with side lengths $AD = 2X$ and $DC = 13X$ . We will use the formula for the area of a rectangle:

$A = \text{length} \times \text{width}$

Here, the length and width of the rectangle are $AD$ and $DC$ . Therefore:

$A = AD \times DC = (2X) \times (13X)$

Step-by-step calculation:

Multiply the coefficients: $2 \times 13 = 26$ .
Combine the variable terms: $X \times X = X^2$ .

Thus, the area of the rectangle is:

$A = 26X^2$

The solution to the problem is $26X^2$ , which corresponds to choice 1.

Final Answer

$26x^2$

Key Points to Remember

Essential concepts to master this topic

Area Formula: Rectangle area equals length times width
Technique: Multiply terms: (2x) × (13x) = 26x²
Check: Verify units match: length × length = area units ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying the dimensions
Don't add 2x + 13x = 15x! This gives perimeter, not area. Area requires multiplication of dimensions. Always multiply length × width to find rectangle area.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why do I multiply the variables x × x to get x²?

When you multiply like variables, you add their exponents. Since x has an implied exponent of 1, we get: $x^1 \times x^1 = x^{1+1} = x^2$

What's the difference between area and perimeter?

Area measures the space inside (multiply dimensions), while perimeter measures the distance around (add all sides). For this rectangle: Area = $26x^2$ , Perimeter = $2(2x + 13x) = 30x$

How do I multiply 2x and 13x step by step?

Break it into parts: coefficients and variables

Multiply numbers: 2 × 13 = 26
Multiply variables: x × x = x²
Combine: $26x^2$

Can the area ever be negative with algebraic expressions?

In real geometry, area is always positive. However, when working with algebraic expressions like $26x^2$ , the sign depends on the value of x. Since x² is always positive for real numbers, this area will always be positive when x ≠ 0.

What if I forgot to include the x² and just wrote 26?

Always keep track of your variables! The area formula gives you $26x^2$ , not just 26. The x² tells you how the area changes as x changes - it's crucial information!

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