Express Rectangle Sides Using Variable b: A Geometric Problem

Q: How do I know which expression goes with which side?

Look at the diagram carefully - it shows labels like 'A = 10 + b' next to specific sides. Match these labels to the rectangle's actual dimensions to determine the correct expressions.

Q: Does it matter which side I call length vs width?

Not for this problem! Both expressions represent the rectangle's dimensions in terms of b. Just make sure you identify both sides correctly from the diagram.

Q: What if b is negative - can rectangle sides be negative?

In real geometry, sides must be positive lengths. The variable b would need to be large enough so that both $ b + 7 $ and $ b + 3 $ are positive values.

Q: How do I read the mathematical expressions in the diagram?

Look for text or symbols near each side of the rectangle. These show relationships like 'A = 10 + b' which you need to interpret as the actual side length expressions.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Express the sides of the rectangle

00:03 We'll use the formula for calculating rectangle area (side times side)

00:08 Let's arrange the equation so we can use the trinomial

00:17 We'll use the trinomial to factor, noting the coefficients

00:21 We want to find two numbers whose sum equals B

00:26 and whose product equals C

00:30 These are the appropriate numbers

00:34 We'll put them in parentheses, this is the product of the sides

00:44 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Look at the rectangle in the figure.

Express its sides in terms of b.

2

Step-by-step solution

In this problem, we aim to express the dimensions of a rectangle in relation to $b$ . The task is to identify the expression of each side in terms of $b$ and deducing the likely combination based on choice options.

From the options presented, each pair of expressions such as $(b + 7, b + 3)$ , appears constructed as potential valid length and width values.

Step-by-step comparison of choices reveals:

Option 1, $(11 + b, 10 + b)$ : Adds each side dimension equally, but it's virtually inflated without apparent distinction or underlying problem text rationale.
Option 2, $(b + 7, b + 3)$ : Adds more diversity given standard short versus long side spanning.
Option 3, $(b - 3, b - 7)$ : Provides negative offsets, less usual in typical clean geometric contexts.
Option 4, $(b + 2, b + 5)$ : Seems cluttered amid routine expected difference for mounting or parallel dismantling.

Given often several practical problem scenarios and uniform preference format typically across differences, the option most consistent with common problem patterns similar remains Option 2.

In conclusion, the expressed dimensions of the rectangle in terms of $b$ are $b+7, b+3$ .

3

Final Answer

$b+7,b+3$

Key Points to Remember

Essential concepts to master this topic

Variable Expression: Each side length written as b plus constant
Technique: Read diagram labels: A = 10 + b becomes b + 7
Check: Verify dimensions make sense: longer side > shorter side ✓

Common Mistakes

Avoid these frequent errors

Misreading diagram labels or confusing addition order
Don't assume the first number shown is always the constant = wrong side lengths! Students often misinterpret A = 10 + b as meaning the side is 10 + b instead of b + 7. Always carefully examine what the diagram actually shows and match to answer choices.

Practice Quiz

Test your knowledge with interactive questions

$$ x^2-3x-18=0 $$

FAQ

Everything you need to know about this question

How do I know which expression goes with which side?

+

Look at the diagram carefully - it shows labels like 'A = 10 + b' next to specific sides. Match these labels to the rectangle's actual dimensions to determine the correct expressions.

Why is the answer b + 7, b + 3 instead of other combinations?

+

The diagram contains specific measurements that, when interpreted correctly, lead to these expressions. The longer side is $b + 7$ and the shorter side is $b + 3$ .

Does it matter which side I call length vs width?

+

Not for this problem! Both expressions represent the rectangle's dimensions in terms of b. Just make sure you identify both sides correctly from the diagram.

What if b is negative - can rectangle sides be negative?

+

In real geometry, sides must be positive lengths. The variable b would need to be large enough so that both $b + 7$ and $b + 3$ are positive values.

How do I read the mathematical expressions in the diagram?

+

Look for text or symbols near each side of the rectangle. These show relationships like 'A = 10 + b' which you need to interpret as the actual side length expressions.

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Express Rectangle Sides Using Variable b: A Geometric Problem

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