Rectangle Area 36: Finding Length AE When AE = 1/4 AB

Q: Why can't I just use the area to find AE directly?

The area formula uses the full length AB, not the partial length AE. You must find AB first using $ Area = length \times width $, then use the given relationship to find AE.

Q: What does $ AE = \frac{1}{4}AB $ actually mean?

This means AE is exactly one-fourth (or 25%) of the total length AB. So if AB = 12, then AE = 12 ÷ 4 = 3.

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

In this problem, the diagram shows the width is 3 units (the vertical side). Since area = 36, you can find the length: $ length = \frac{36}{3} = 12 $.

Q: Can I check my answer another way?

Yes! Since AE = 3 and AB = 12, check that $ \frac{3}{12} = \frac{1}{4} $. Also verify the rectangle area: length × width = 12 × 3 = 36 ✓

Rectangle Area with Fractional Side Relationships

The area of the rectangle below is equal to 36.

$AE=\frac{1}{4}AB$

Calculate the size of AE.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find AE

00:04 The formula for calculating rectangle area is length (AC) times width (AB)

00:10 Let's substitute appropriate values and solve for AB

00:19 This is the size of AB

00:22 AE equals one-fourth of AB according to the given data

00:25 And this is the solution to the question

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 36.

$AE=\frac{1}{4}AB$

Calculate the size of AE.

Step-by-step solution

The area of rectangle ABCD equals its length multiplied by its width.

Let's input the known data into the formula in order to find side AB:

$36=3\times AB$

Now, let's divide both sides by 3:

$AB=12$

Since we know that AE equals a quarter of AB, we can substitute the known data into the formula to calculate side AE:

$AE=\frac{1}{4}AB=\frac{1}{4}\times12=3$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Rectangle area equals length times width
Technique: Use $36 = 3 \times AB$ to find AB = 12
Check: Verify $AE = \frac{1}{4} \times 12 = 3$ matches given ratio ✓

Common Mistakes

Avoid these frequent errors

Using the fraction relationship before finding the full side length
Don't try to find AE directly from the area without first calculating AB = wrong approach! You need the complete side length first. Always find the full side AB using area ÷ width, then apply the fraction $AE = \frac{1}{4}AB$ .

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 can't I just use the area to find AE directly?

The area formula uses the full length AB, not the partial length AE. You must find AB first using $Area = length \times width$ , then use the given relationship to find AE.

What does $AE = \frac{1}{4}AB$ actually mean?

This means AE is exactly one-fourth (or 25%) of the total length AB. So if AB = 12, then AE = 12 ÷ 4 = 3.

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

In this problem, the diagram shows the width is 3 units (the vertical side). Since area = 36, you can find the length: $length = \frac{36}{3} = 12$ .

Can I check my answer another way?

Yes! Since AE = 3 and AB = 12, check that $\frac{3}{12} = \frac{1}{4}$ . Also verify the rectangle area: length × width = 12 × 3 = 36 ✓

What if the fraction was different, like $AE = \frac{1}{3}AB$ ?

The process stays the same! First find AB from the area, then multiply by the fraction. If $AE = \frac{1}{3}AB$ and AB = 12, then $AE = \frac{1}{3} \times 12 = 4$ .

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Rectangle Area 36: Finding Length AE When AE = 1/4 AB

Rectangle Area with Fractional Side Relationships

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I just use the area to find AE directly?

What does $AE = \frac{1}{4}AB$ actually mean?

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

Can I check my answer another way?

What if the fraction was different, like $AE = \frac{1}{3}AB$ ?

🌟 Unlock Your Math Potential

More Questions

Area of a Rectangle

Calculate EB Length When EB = 1/5 AB in a Rectangle with Area 70

Calculate ED Length When ED = 1/3 AB in Rectangle with Area 45

Rectangle Area Problem: Finding EBFD When EB=1/4AB and Area=16

Rectangle Area Problem: Finding EBFD Area Using 1/7 Ratio and Parallel Lines

Rectangle Area 36: Finding Length AE When AE = 1/4 AB

Rectangle Area with Fractional Side Relationships

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I just use the area to find AE directly?

What does AE=14AB AE = \frac{1}{4}AB AE=41​AB actually mean?

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

Can I check my answer another way?

What if the fraction was different, like AE=13AB AE = \frac{1}{3}AB AE=31​AB?

🌟 Unlock Your Math Potential

More Questions

Area of a Rectangle

Calculate EB Length When EB = 1/5 AB in a Rectangle with Area 70

Calculate ED Length When ED = 1/3 AB in Rectangle with Area 45

Rectangle Area Problem: Finding EBFD When EB=1/4AB and Area=16

Rectangle Area Problem: Finding EBFD Area Using 1/7 Ratio and Parallel Lines

What does $AE = \frac{1}{4}AB$ actually mean?

What if the fraction was different, like $AE = \frac{1}{3}AB$ ?