# Thread: area of a rectangle

1. ## area of a rectangle

suppose the expression x^2+7x+12/(x+2)^2 represents the area of a rectangle

find the expression for the perimeter of the rectangle

2. Originally Posted by william
suppose the expression x^2+7x+12/(x+2)^2 represents the area of a rectangle

find the expression for the perimeter of the rectangle
What does x represent? The length of a side ....?

And is it $A = x^2 + 7x + \frac{12}{(x+2)^2}$ or $A = \frac{ x^2 + 7x + 12}{(x+2)^2}$ ?

3. Originally Posted by mr fantastic
What does x represent? The length of a side ....?

And is it $A = x^2 + 7x + \frac{12}{(x+2)^2}$ or $A = \frac{ x^2 + 7x + 12}{(x+2)^2}$ ?
The question says suppose the expression represents the area of a rectangle, find the expression for the perimeter of the rectangle. And it is the second equation, where 7x and x^2 are included in the numerator.

4. Originally Posted by william
The question says suppose the expression represents the area of a rectangle, find the expression for the perimeter of the rectangle. And it is the second equation, where 7x and x^2 are included in the numerator.
A = xy => y = A/x and you're given A. Then:

Perimeter = 2x + 2y.

5. Originally Posted by mr fantastic
A = xy => y = A/x and you're given A. Then:

Perimeter = 2x + 2y.
I am not exactly sure of what you are suggesting. Can you be a little more specific?

My ideas on the question: factor the top: (x+4)(x+3)/(x+2)(x+2)
then split it into two expressions?

6. Originally Posted by william
I am not exactly sure of what you are suggesting. Can you be a little more specific?

My ideas on the question: factor the top: (x+4)(x+3)/(x+2)(x+2)
then split it into two expressions?
You're given an expression for A. Divide that expression by x to get the other side of the rectangle: y = A/x.

Then perimeter = x + x + y + y = 2x + 2y and the problem is answered.

7. Originally Posted by mr fantastic
You're given an expression for A. Divide that expression by x to get the other side of the rectangle: y = A/x.

Then perimeter = x + x + y + y = 2x + 2y and the problem is answered.
Unless it's something really really stupid like you're expected to say

$A = \frac{(x+3)(x+4)}{(x+2)(x+2)} = \left(\frac{x+3}{x+2}\right) \cdot \left(\frac{x+4}{x+2}\right)$

and then you're meant to take $\frac{x+3}{x+2}$ as the length and $\frac{x+4}{x+2}$ as the width.

Which is why I asked what x was.

In which case all I can say is and hope that whoever set the question accidently sets their pants on fire.

8. Originally Posted by mr fantastic
Unless it's something really really stupid like you're expected to say

$A = \frac{(x+3)(x+4)}{(x+2)(x+2)} = \left(\frac{x+3}{x+2}\right) \cdot \left(\frac{x+4}{x+2}\right)$

and then you're meant to take $\frac{x+3}{x+2}$ as the length and $\frac{x+4}{x+2}$ as the width.

Which is why I asked what x was.

In which case all I can say is and hope that whoever set the question accidently sets their pants on fire.
haha! this is what i was thinking, but did not think it was that simple, although now I think it is, thank you for your help!

9. Originally Posted by mr fantastic
Unless it's something really really stupid like you're expected to say

$A = \frac{(x+3)(x+4)}{(x+2)(x+2)} = \left(\frac{x+3}{x+2}\right) \cdot \left(\frac{x+4}{x+2}\right)$

and then you're meant to take $\frac{x+3}{x+2}$ as the length and $\frac{x+4}{x+2}$ as the width.

Which is why I asked what x was.

In which case all I can say is and hope that whoever set the question accidently sets their pants on fire.
Then I would simply multiply (x+3/x+2) and (x+4/x+2) by two and then add them together, correct? Final being 2x^2+14/x^2+4

10. Originally Posted by william
Then I would simply multiply (x+3/x+2) and (x+4/x+2) by two and then add them together, correct? Final being 2x^2+14/x^2+4
Yes. And the fool who wrote the question will probably want you to simplify the answer.

But 2x^2+14/x^2+4 is not correct. I get $\frac{4x+14}{x+2}$.

11. Originally Posted by mr fantastic
Yes. And the fool who wrote the question will probably want you to simplify the answer.

But 2x^2+14/x^2+4 is not correct. I get $\frac{4x+14}{x+2}$.
i multiplied the expression to get (x^2+6/x^2+4) + (x^2+8/x^2+4) add the numerators and the denominator stays the same? what did i do wrong?

12. Originally Posted by william
i multiplied the expression to get (x^2+6/x^2+4) + (x^2+8/x^2+4) add the numerators and the denominator stays the same? what did i do wrong?
$P = 2 \left(\frac{x+3}{x+2}\right) + 2 \left(\frac{x+4}{x+2}\right) = \frac{2(x+3) + 2(x+4)}{x+2} = \, ....$

13. Originally Posted by mr fantastic
$P = 2 \left(\frac{x+3}{x+2}\right) + 2 \left(\frac{x+4}{x+2}\right) = \frac{2(x+3) + 2(x+4)}{x+2} = \, ....$
I really appreciate the help, you are very kind!