Rectangle Area Problem: Finding Width When Area = 15 and Height = 2.5

Q: Why do we divide instead of multiply?

Because we're working backwards from the area formula! We know Area = length × width, so to find a missing side, we divide the area by the known side.

Q: Can I use different formulas for rectangles?

The basic area formula $ A = l \times w $ is the most important one. Other formulas like perimeter use addition, but for area problems, always use multiplication.

Q: How can I remember the rectangle area formula?

Think of it as "how many unit squares fit inside". If you have 6 squares across and 2.5 squares down, you have 6 × 2.5 = 15 total squares!

Rectangle Formulas with Given Area

The area of the rectangle below is equal to 15.

AC = 2.5

Calculate 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 Insert the relevant values into the formula according to the given data and solve for AB

00:12 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 15.

AC = 2.5

Calculate AB.

Step-by-step solution

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

Let's begin by inserting the known data into the formula:

$S=AB\times AC$

$15=AB\times2.5$

Let's now divide both sides by 2.5:

$AB=6$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area of rectangle equals length times width
Technique: Divide area by known dimension: 15 ÷ 2.5 = 6
Check: Multiply dimensions back together: 6 × 2.5 = 15 ✓

Common Mistakes

Avoid these frequent errors

Confusing which dimension to use in calculations
Don't use AB when you should use AC = 2.5 in your calculation! This mixes up the dimensions and gives wrong results. Always identify which measurement corresponds to which side before substituting into Area = length × width.

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

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

It doesn't matter which you call length or width! What matters is using the correct measurements. In this problem, AC = 2.5 and we need to find AB.

Why do we divide instead of multiply?

Because we're working backwards from the area formula! We know Area = length × width, so to find a missing side, we divide the area by the known side.

What if I get a decimal answer?

Decimal answers are perfectly normal in geometry! Just make sure to check your work by multiplying your answer back with the given dimension.

Can I use different formulas for rectangles?

The basic area formula $A = l \times w$ is the most important one. Other formulas like perimeter use addition, but for area problems, always use multiplication.

How can I remember the rectangle area formula?

Think of it as "how many unit squares fit inside". If you have 6 squares across and 2.5 squares down, you have 6 × 2.5 = 15 total squares!

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