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

Q: Why do I need to find CD first before calculating ED?

Because the problem states ED = 1/3 AB, and in rectangles, opposite sides are equal. So AB = CD. You must find CD using the area formula, then use that value for AB in the fraction.

Q: How do I know which sides are equal in a rectangle?

Opposite sides are always equal in rectangles. So AB = CD and AC = BD. Look at the diagram to identify which sides are opposite to each other.

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

No, the area is the key information that lets you find the unlabeled side CD. Without using Area = length × width = 45, you can't determine what AB equals.

Q: How do I verify my answer is correct?

Check two things: Does 5 × 9 = 45? ✓Does 3 = 1/3 × 9? ✓ Both should be true for your answer to be correct.

Rectangle Properties with Fractional Relationships

The area of the rectangle below is equal to 45.

$ED=\frac{1}{3}AB$

Calculate the size of ED.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's find the length of ED.

00:12 To find the rectangle's area: multiply the length, AC, by the width, AB.

00:19 Now, let's plug in the values and solve for AB.

00:29 We're told that ED is one-third of AB.

00:33 And that's how we solve this problem!

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 45.

$ED=\frac{1}{3}AB$

Calculate the size of ED.

Step-by-step solution

The area of rectangle ABCD equals length times width.

Let's write down the known data in a formula to find side CD:

$45=5\times CD$

Let's divide both sides by 5:

$CD=9$

We know that in a rectangle, each pair of opposite sides are equal, therefore:

$AB=CD=9$

Since we are given that ED equals one-third of CD, we can substitute the known data and calculate side ED:

Remember that AB equals CD

$ED=\frac{1}{3}AB=\frac{1}{3}\times9=3$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Rectangle area equals length times width (A = l × w)
Technique: Use area 45 = 5 × width to find CD = 9
Check: Verify $ED = \frac{1}{3} \times 9 = 3$ matches given relationship ✓

Common Mistakes

Avoid these frequent errors

Using ED = 1/3 of the given side length
Don't calculate ED as 1/3 of the labeled side (1/3 × 5 = 1.67) = wrong answer! This ignores which side AB actually represents. Always identify that AB equals the unlabeled side CD first, then apply the fraction.

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 I need to find CD first before calculating ED?

Because the problem states ED = 1/3 AB, and in rectangles, opposite sides are equal. So AB = CD. You must find CD using the area formula, then use that value for AB in the fraction.

How do I know which sides are equal in a rectangle?

Opposite sides are always equal in rectangles. So AB = CD and AC = BD. Look at the diagram to identify which sides are opposite to each other.

What if I calculated ED as 1/3 of the side labeled 5?

That's incorrect! The side labeled 5 is AC, not AB. The relationship ED = 1/3 AB means you need AB's length, which equals CD = 9, not the labeled side of 5.

Can I solve this without using the area formula?

No, the area is the key information that lets you find the unlabeled side CD. Without using Area = length × width = 45, you can't determine what AB equals.

How do I verify my answer is correct?

Check two things:

Does 5 × 9 = 45? ✓
Does 3 = 1/3 × 9? ✓

Both should be true for your answer to be correct.

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