5th grade math

Question

I have the area of a rectangle of 864 and I know that my width is 2/3rd the length of my length.  How do I find my width?

 

Answer 1

Hi Lynn--

 

As a 5th grader you might not know about square roots yet. If not, try factoring 864.

 

The idea is to find 2 numbers that multiply to 864, and one of those numbers is 2/3 of the other.

 

So, do some factor pairs:

 

1 x 864

 

2 x 432

 

3 x 288 (how do you know these? just keep dividing 864 by the next number. 864 divided by 3 = 288. If you divide 864 by a number and get a remainder, then that number is NOT a factor of 864. Skip it!)

 

4 x 216

 

and keep going for a bit.

 

Every few times, stop and see if one number is 2/3 of the other. "But wait, how do I do that?"

 

Divide the bigger number by 3, which will give you 1/3 of it. Then double that number, and if it equals the smaller one, you're done!

 

Example: if one of our factor pairs is 8 x 108, and we want to see if 8 is 2/3 of 108, we do 108 divided by 3, which is 36. Double that to get 72, which is not 8, so we have to keep going.

 

let's save you some time here.

 

If I keep trying factor pairs, eventually I will get to the number 24. So I will try 864 divided by 24.

 

What number do you get? and is 24 equal to 2/3 of that number. (Divide the number you got by 3, to get 1/3. Now double it--is that number 24? You're done!

 

If you're still stuck, post back and I'll help you out. :-)

 

Good luck,

 

Matt in NY

Answer 2

Hi Lynn,

 

As always, whenever you are finding a value of something, anything, start by giving it a name. Lets call the width w. What do we know about width w? w=2/3l   (l is the length).

 

What else do we know? we know that area of a rectangle is A=w*l=864

 

We now substitute 2/3l where w is in the formula and get A=2/3l*l=2/3l²=864

 

multiply through by 3 and divide by 2 and you get l²=3/2(864)=1296

 

l = sqrt(1296)

 

Try the same problem by first solving for l from the equation, which by the way, is easier than what I just did.

hope this helps