## Comment on Radius vs. Diameter

### When you divide both sides by

When you divide both sides by b in the last step to get root 2 and 2, How you make sure that b is not negative?﻿

### Good question.

Good question.
b represents the radius of Circle B, and the radius of a circle will always be positive.

### Hi Brent,

Hi Brent,
I solved it this way.
circle A area = Pie *(r square)
circle B area = 2* pie * r square
Pie *(r square) = 2* pie * r square (as per shared info)

comparing these both areas. (used matching operations)

divide by pie to both quantities to get

r square (qty A)

2 r square (qty B)

divided by 2 to both quantities:
r square/2 (qty A)
r square(qty B)
take sq. root of both quantities:
sq root(r square/2) (qty A)
r (qty B)
r/sq. root 2 (qty A) can be rewritten as r*sq root 2/2

Now multiplied both sides by 2 to get:
r*sq root 2 (qty A)
2*r (qty B) which is nothing but diameter of Qty B.
Since 2*r is greater than sq root 2* r , so qty B is greater than qty A. Is this approach correct?

### I'm not sure I follow your

What does r represent?
I ask because your equation πr² = 2πr² boils down to saying 1 = 2.

I think it would be useful to assign a different variable to the radius of each circle.

### Yes right,(with due respect)

Yes right,(with due respect) using 2 different variables will avoid unwanted confusions.

I meant , πr² = 2πr² because area of circle A is twice the area of circle B so I wrote it as , πr² = 2πr² and solved further, but yes, it boils down to saying, 1=2 which is not a perfectly sound equation. So how will I know in such QC questions whether to use one variable or 2? Because using one variable I still got the answer.

### Your question: So how will I

Your question: So how will I know in such QC questions whether to use one variable or 2?

We can use one variable to create more than one variable expressions as long as the variable represents the SAME VALUE for all expressions.

Here's what I mean:

JOON IS 5 YEARS OLDER THAN MAX
If we let x = Max's age...
Then x+5 = Joon's age

In both cases, x represents Max's age. So, it's okay to use one variable.

In your example, you used r to represent two DIFFERENT VALUES (the radius of the small circle AND the radius of the large circle.

Does that help?

Cheers,
Brent

### Makes perfect sense. thanks a

Makes perfect sense. thanks a ton Brent :) You are genius.

### Hi Mr hanneson,

Hi Mr Hanneson,

I plugged in some nice value for the area of circle B and I found the values of both the radii and then I figured out the answer by multiplying the radius of circle B by 2.

Did I do it right?

### That's a great approach,

That's a great approach, Abdul.

Cheers,
Brent

### I tried plugging in and I got

I tried plugging in and I got a strange result.
I said area A = 4π
I said area B = 2π

Then when I multiplied radius B by 2 to get diameter B:
diameter B = 2√2

Shouldn't I end up with 2 vs √2?

I must have made a mistake somewhere, but I don't see it. Could you please take a look.