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

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

In this problem, it doesn't matter! Rectangle area is length × width, so whether AB is length or width, the calculation works the same way. Focus on finding the complete side length first.

Q: What does EB = 1/5 AB actually mean in the diagram?

Point E divides side AB into two parts: AE and EB. Since $ EB = \frac{1}{5}AB $, then $ AE = \frac{4}{5}AB $. So E is located 4/5 of the way from A to B.

Rectangle Area with Fractional Segments

The area of the rectangle is 70.

$EB=\frac{1}{5}AB$

Calculate the length of EB.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find EB

00:03 The formula for calculating rectangle area is length (AC) times width (AB)

00:09 Let's substitute appropriate values and solve for AB

00:19 This is the size of AB

00:22 EB equals one-fifth of AB according to the given data

00:26 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The area of the rectangle is 70.

$EB=\frac{1}{5}AB$

Calculate the length of EB.

Step-by-step solution

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

Let's substitute the known values into the formula:

$70=7\times AB$

Now let's divide both sides by 7:

$AB=10$

Since we know that EB equals one-fifth of AB, we can use the known data to calculate side EB as follows:

$EB=\frac{1}{5}AB=\frac{1}{5}\times10=2$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Rectangle area equals length times width
Technique: From 70 = 7 × AB, divide both sides: AB = 10
Check: EB = 1/5 × 10 = 2, verify AB = AE + EB = 8 + 2 = 10 ✓

Common Mistakes

Avoid these frequent errors

Confusing which dimension to use for calculation
Don't use EB directly in area formula = wrong setup! The area formula needs the full rectangle dimensions (length and width), not partial segments. Always identify the complete rectangle sides first, then calculate the fractional segment.

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

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

In this problem, it doesn't matter! Rectangle area is length × width, so whether AB is length or width, the calculation works the same way. Focus on finding the complete side length first.

What does EB = 1/5 AB actually mean in the diagram?

Point E divides side AB into two parts: AE and EB. Since $EB = \frac{1}{5}AB$ , then $AE = \frac{4}{5}AB$ . So E is located 4/5 of the way from A to B.

Why can't I just use the area 70 and the given side 7 to find EB directly?

Because EB is not a complete side of the rectangle! You need the full side length AB first. Then use the relationship $EB = \frac{1}{5}AB$ to find the segment.

How do I check if my answer of 2 is correct?

Verify two ways: 1) Check that AB = 10 gives area: 7 × 10 = 70 ✓ 2) Check the fraction: $\frac{1}{5} \times 10 = 2$ ✓

What if the fraction was different, like EB = 1/3 AB?

The method stays the same! First find AB using the area formula, then apply whatever fraction is given. If $EB = \frac{1}{3}AB$ and AB = 10, then $EB = \frac{1}{3} \times 10 = \frac{10}{3}$ .

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