# Thread: Rectangle's Dimensions

1. ## Rectangle's Dimensions

A rectangle has a perimeter of 23cm. Its area is 33cm². Determine the dimensions of the rectangle.

Can anyone help?

2. Originally Posted by xcompulsion
A rectangle has a perimeter of 23cm. Its area is 33cm². Determine the dimensions of the rectangle.

Can anyone help?
Perimeter:

$2l + 2w = 23$.

Area:

$l\,w = 33$.

Solve these equations simultaneously.

3. Originally Posted by Prove It
Perimeter:

$2l + 2w = 23$.

Area:

$l\,w = 33$.

Solve these equations simultaneously.
Hi again, could you maybe help me start it off?

4. Originally Posted by xcompulsion
Hi again, could you maybe help me start it off?
Use one of the equations to isolate a variable, then substitute that into the other equation, for example

$lw = 33$

$l = \frac{33}{w}$

Substitute:

$2l + 2w = 23$

$2\left(\frac{33}{w}\right) + 2w = 23$

$66 + 2w^2 = 23w$

Solve for $w$, then use either equation to find $l$ given $w$.

5. Originally Posted by undefined
Use one of the equations to isolate a variable, then substitute that into the other equation, for example

$lw = 33$

$l = \frac{33}{w}$

Substitute:

$2l + 2w = 23$

$2\left(\frac{33}{w}\right) + 2w = 23$

$66 + 2w^2 = 23w$

Solve for $w$, then use either equation to find $l$ given $w$.
okay so after solving for w,

$66 + 2w^2 = 23w$

$66 + 2w^2 - 23w = 0$

$(w - 6)(w - 5.5) = 0$

so does w = 6, or 5.5?

6. This just means that there are two rectangles that could have these dimensions.

Substitute both into the perimeter formula and solve for $l$.

7. Originally Posted by Prove It
This just means that there are two rectangles that could have these dimensions.

Substitute both into the perimeter formula and solve for $l$.
Substitute both of them? I'm sorry, I don't really understand.

8. Originally Posted by xcompulsion
Substitute both of them? I'm sorry, I don't really understand.
If you take $w = 6$, you will get $l = 5.5$.

If you take $w = 5.5$, you will get $l = 6$.

You get the same rectangle either way :-)

9. Originally Posted by xcompulsion
Substitute both of them? I'm sorry, I don't really understand.
Substitute one of them into the equation. Solve for $l$.

Then pretend you hadn't done that, and substitute the second into the equation. Solve for $l$.

10. Oh! Okay, I understand now.

Thanks a lot.