Rectangle Area Problem: Find Width AB When Area = 75 and Height = 7.5

Q: Why do I divide the area by the height?

Because the area formula is A = length × width. If you know the area and one dimension, you can find the other by reversing the multiplication: unknown dimension = area ÷ known dimension.

Q: How do I handle the decimal 7.5 in the division?

Treat it like any division problem: $ 75 ÷ 7.5 = 10 $. You can also think of it as $ \frac{75}{7.5} = \frac{750}{75} = 10 $.

Q: Can I check my answer a different way?

Yes! Multiply your answer by the given dimension: AB × AC = 10 × 7.5 = 75. If this equals the given area, you're correct!

Rectangle Area with Fractional Dimensions

The area of the rectangle is equal to 75.

AC = 7.5

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)

00:08 Insert the relevant values into the formula according to the given data and solve for AB

00:13 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 is equal to 75.

AC = 7.5

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:

$S=AB\times AC$

$75=AB\times7.5$

Let's now divide both sides by 7.5:

$AB=10$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals length times width (A = l × w)
Technique: Divide area by known dimension: 75 ÷ 7.5 = 10
Check: Verify by multiplying: 10 × 7.5 = 75 ✓

Common Mistakes

Avoid these frequent errors

Confusing which dimension to use for calculation
Don't multiply 75 × 7.5 = 562.5! This assumes you're finding area when you already have it. Always divide the area by the known dimension to find the unknown dimension.

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 divide the area by the height?

Because the area formula is A = length × width. If you know the area and one dimension, you can find the other by reversing the multiplication: unknown dimension = area ÷ known dimension.

What if I get confused about which side is length vs width?

It doesn't matter! In rectangles, you can call either dimension length or width. What matters is that area = one side × the other side.

How do I handle the decimal 7.5 in the division?

Treat it like any division problem: $75 ÷ 7.5 = 10$ . You can also think of it as $\frac{75}{7.5} = \frac{750}{75} = 10$ .

Can I check my answer a different way?

Yes! Multiply your answer by the given dimension: AB × AC = 10 × 7.5 = 75. If this equals the given area, you're correct!

What if my answer comes out as a fraction or decimal?

That's perfectly normal! Rectangle dimensions can be any positive number. Just make sure to simplify fractions or round decimals appropriately if asked.

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