Rectangle Area Problem: Finding Side Length When Area = 55 and Height = 5.5

Q: Why do we divide 55 by 5.5 instead of subtracting?

Because area equals length × width. If 55 = AB × 5.5, then to find AB, we divide both sides by 5.5. Subtraction would only work if we were finding perimeter!

Q: Can I solve this without using the area formula?

No, the area formula is essential here! We're told the area is 55 and one side is 5.5. The only way to find the unknown side is using $ Area = length \times width $.

Rectangle Area Formula with Division Method

The area of the rectangle below is equal to 55.

AC = 5.5

Calculate the length of side AB.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the value of AB

00:03 The formula for calculating the area of a rectangle is width(AB) multiplied by length(AC)

00:07 Substitute the relevant values into the formula according to the given data and proceed to solve for AB

00:14 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The area of the rectangle below is equal to 55.

AC = 5.5

Calculate the length of side AB.

Step-by-step solution

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

Hence let's begin by inserting the known data into the formula:

$S=AB\times AC$

$55=AB\times5.5$

Let's now divide both sides by 5.5:

$AB=10$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area = length × width for all rectangles
Technique: Isolate unknown by dividing: 55 ÷ 5.5 = 10
Check: Verify: 10 × 5.5 = 55 square units ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't calculate 55 - 5.5 = 49.5! Area requires multiplication of dimensions, not subtraction. This gives a completely wrong answer. Always use Area = length × width and solve by dividing the area by the known dimension.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why do we divide 55 by 5.5 instead of subtracting?

Because area equals length × width. If 55 = AB × 5.5, then to find AB, we divide both sides by 5.5. Subtraction would only work if we were finding perimeter!

What if I get a decimal answer instead of a whole number?

That's completely normal! Rectangle dimensions can be decimals. Just make sure your decimal is accurate and always check by multiplying back: your answer × 5.5 should equal 55.

How do I remember which dimension is length vs width?

It doesn't matter which you call length or width! In rectangles, you just need two perpendicular sides. AB and AC are perpendicular, so AB × AC = 55 works perfectly.

Can I solve this without using the area formula?

No, the area formula is essential here! We're told the area is 55 and one side is 5.5. The only way to find the unknown side is using $Area = length \times width$ .

What if I accidentally multiply 55 × 5.5?

You'd get 302.5, which is way too big! Remember: we need to work backwards from the area. Since Area ÷ known side = unknown side, we divide, not multiply.

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