Calculate Rectangle Side Length: Finding AB When Area = 132 and AC = 8.5

Q: How do I know which sides to multiply for area?

For rectangles, area = length × width. It doesn't matter which side you call length or width - just multiply any two adjacent (touching) sides. Here, AB and AC are adjacent sides.

Q: Why do I divide 132 by 8.5 instead of adding?

Because we're undoing multiplication! Since area = AB × 8.5, we use the opposite operation (division) to find AB: AB = 132 ÷ 8.5 = 15.

Q: What if I get a decimal answer?

Decimal answers are perfectly valid! Just make sure to check your work by multiplying back: if your answer × 8.5 equals 132, you're correct.

Q: Can I use the Pythagorean theorem here?

No! The Pythagorean theorem is for finding diagonal lengths in right triangles. This problem gives you the area and one side, so use the area formula instead.

Q: How do I check if 15 is really correct?

Substitute back into the area formula: $ 15 \times 8.5 = 127.5 + 4.5 = 132 $ ✓ Since this matches the given area, AB = 15 is correct!

Rectangle Area Formula with Given Diagonal

The area of the rectangle below is equal to 132.

AC = 8.5

Calculate length of side 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 Substitute in the relevant values 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 below is equal to 132.

AC = 8.5

Calculate length of side 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:

$S=AB\times AC$

$132=AB\times8.5$

Let's now divide both sides by 8.5:

$AB=15$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Rectangle area equals length times width
Substitution: Replace known values: 132 = AB × 8.5
Verification: Check answer: 15 × 8.5 = 132 ✓

Common Mistakes

Avoid these frequent errors

Confusing which sides to multiply
Don't assume AC is the length when it might be the width = wrong setup! Students often guess randomly which measurement goes where. Always identify that area = any side × adjacent side, so 132 = AB × AC.

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 sides to multiply for area?

For rectangles, area = length × width. It doesn't matter which side you call length or width - just multiply any two adjacent (touching) sides. Here, AB and AC are adjacent sides.

Why do I divide 132 by 8.5 instead of adding?

Because we're undoing multiplication! Since area = AB × 8.5, we use the opposite operation (division) to find AB: AB = 132 ÷ 8.5 = 15.

What if I get a decimal answer?

Decimal answers are perfectly valid! Just make sure to check your work by multiplying back: if your answer × 8.5 equals 132, you're correct.

Can I use the Pythagorean theorem here?

No! The Pythagorean theorem is for finding diagonal lengths in right triangles. This problem gives you the area and one side, so use the area formula instead.

How do I check if 15 is really correct?

Substitute back into the area formula: $15 \times 8.5 = 127.5 + 4.5 = 132$ ✓ Since this matches the given area, AB = 15 is correct!

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