Find X in Rectangle Area: Solving When Area = 28 and Height = 4

Q: Why can't I just divide 28 by 4 to get 7, then solve x + 5 = 7?

You actually can! That's a perfectly valid approach. Since $ 28 = 4 \times (x + 5) $, dividing both sides by 4 gives $ 7 = x + 5 $, so x = 2. Both methods work!

Q: How do I know which side is length and which is width?

It doesn't matter! Rectangle area is length × width, and since multiplication is commutative, you get the same result either way. Just pick one dimension for length and the other for width.

Q: Can I use FOIL to solve this problem?

FOIL isn't needed here since we have 4 times a binomial, not two binomials multiplied. Use the distributive property: $ 4(x + 5) = 4x + 20 $.

Q: Why does the diagram show AB = X + 5 but we use x + 5 in lowercase?

In mathematics, we typically use lowercase letters for variables in equations. The diagram uses uppercase X for labeling, but when writing the equation, we use lowercase x. They represent the same unknown value!

Rectangle Area with Algebraic Dimensions

If the area of the rectangle below is equal to 28.

AC = 4

AB = X + 5

Calculate X.

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Step-by-step video solution

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Step-by-step written solution

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Understand the problem

If the area of the rectangle below is equal to 28.

AC = 4

AB = X + 5

Calculate X.

Step-by-step solution

The area of the rectangle is equal to the length multiplied by the width.

Let's present the known data:

$28=4\times(x+5)$

$28=4x+20$

We'll move 20 to the left side and maintain the appropriate sign:

$28-20=4x$

$8=4x$

Let's divide both sides by 4:

$x=2$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Rectangle area equals length times width exactly
Technique: Set up $28 = 4 \times (x + 5)$ and solve
Check: Substitute x = 2: area = 4 × 7 = 28 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply before isolating the variable
Don't solve $28 = 4 \times (x + 5)$ by dividing 28 by 4 first = wrong setup! This skips the distributive property and gives x = 2 instead of x = 2. Always multiply out 4(x + 5) = 4x + 20 first, then solve the linear equation properly.

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 can't I just divide 28 by 4 to get 7, then solve x + 5 = 7?

You actually can! That's a perfectly valid approach. Since $28 = 4 \times (x + 5)$ , dividing both sides by 4 gives $7 = x + 5$ , so x = 2. Both methods work!

How do I know which side is length and which is width?

It doesn't matter! Rectangle area is length × width, and since multiplication is commutative, you get the same result either way. Just pick one dimension for length and the other for width.

What if I get a negative answer for x?

Check your arithmetic! In this problem, x should be positive since dimensions must be positive. A negative x would mean a negative side length, which doesn't make sense for a real rectangle.

Can I use FOIL to solve this problem?

FOIL isn't needed here since we have 4 times a binomial, not two binomials multiplied. Use the distributive property: $4(x + 5) = 4x + 20$ .

Why does the diagram show AB = X + 5 but we use x + 5 in lowercase?

In mathematics, we typically use lowercase letters for variables in equations. The diagram uses uppercase X for labeling, but when writing the equation, we use lowercase x. They represent the same unknown value!

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