Rectangle Perimeter: Solve for X When Area = 20 and Height = 4

Q: What if I get x = 4 but forget to add 1?

This is a common mistake! Remember that the side length is (x+1), not just x. So when x = 4, the actual side length is 4 + 1 = 5.

Q: Why is the perimeter 18 and not 20?

Don't confuse the area value with the perimeter! Area = 20 is given information. Perimeter = 2(5) + 2(4) = 18 is what we calculate from the side lengths.

Rectangle Problems with Area-Perimeter Calculations

Look at the following rectangle:

The area of the rectangle is 20.

What is the perimeter of rectangle ABCD?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the perimeter of the rectangle

00:05 Apply the formula for calculating the area of a rectangle (side x side)

00:12 Substitute in the relevant values according to the given data and proceed to solve for X

00:33 Open the parentheses, multiply by each factor

00:48 Isolate X

01:02 This is the value of X, substitute in the relevant values to determine the side length

01:10 Opposite sides are equal in a rectangle

01:26 The perimeter of the rectangle equals the sum of its sides

01:32 Substitute the relevant values into the formula and solve for the perimeter

01:50 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following rectangle:

The area of the rectangle is 20.

What is the perimeter of rectangle ABCD?

Step-by-step solution

The area of the rectangle equals its length multiplied by its width:

$S=AB\times AD$

Let's first substitute the data into the formula:

$20=4\times(x+1)$

$20=4x+4$

$20-4=4x$

$16=4x$

$4=x$

Now we can calculate side AB:

$4+1=5$

The perimeter of the rectangle equals the sum of its sides.

Since each pair of opposite sides are equal in a rectangle, we can calculate that:

$AD=BC=4$

$AB=CD=5$

Finally, let's add all the sides together to find the perimeter:

$4+5+4+5=8+10=18$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Rectangle area equals length times width (A = l × w)
Technique: From 20 = 4(x+1), solve: 20 = 4x + 4, so x = 4
Check: Length = 5, width = 4, so area = 5 × 4 = 20 ✓

Common Mistakes

Avoid these frequent errors

Confusing area and perimeter formulas
Don't use perimeter formula P = 2(l + w) when given area information = wrong setup! This leads to incorrect equations with no solution. Always identify what's given (area = l × w) and what's asked (perimeter = 2l + 2w).

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?

FAQ

Everything you need to know about this question

Why do I need to solve for x first instead of finding perimeter directly?

You can't find the perimeter without knowing the actual side lengths! Since one side is (x+1), you must solve for x using the area formula, then calculate the real dimensions.

How do I know which sides are length and width?

In rectangles, it doesn't matter which you call length or width - the area formula A = l × w works either way. Just be consistent: area = 4 × (x+1) = 20.

What if I get x = 4 but forget to add 1?

This is a common mistake! Remember that the side length is (x+1), not just x. So when x = 4, the actual side length is 4 + 1 = 5.

Can I check my answer without calculating the full perimeter?

Yes! First verify the area: length × width = 5 × 4 = 20 ✓. If the area checks out, your dimensions are correct and you can confidently find the perimeter.

Why is the perimeter 18 and not 20?

Don't confuse the area value with the perimeter! Area = 20 is given information. Perimeter = 2(5) + 2(4) = 18 is what we calculate from the side lengths.

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