A floor has two square-shaped designs. The area of the second square-shaped design is nine times greater than the area of the first square-shaped design. Which statement gives the correct relationship between the lengths of the sides of the two squares?

Question

anonymous · Answer

these are the options...

The length of the side of the second square is 3 times greater than the length of the side of the first square. 

 The length of the side of the second square is 12 times greater than the length of the side of the first square. 

 The length of the side of the second square is 9 times greater than the length of the side of the first square. 

 The length of the side of the second square is 6 times greater than the length of the side of the first square.

anonymous · Answer

since $A=l^2$ and $A'=l'^2$
when  $A=9A'$
sub them in to get the relationship between l and  l'

anonymous · Answer

what am i supposed to sub in?

anonymous · Answer

the l and l '
like this: 
$A=9A'$
$l^2 = 9 l'^2$

anonymous · Answer

im like really slow and have no idea wut im doing.-_-

anonymous · Answer

lol. i guess i'll try to do it step by step.
since $A=l^2$, 
$A_1=l_1^2$   (this is the first square)............(1)
$A_2=l_2^2$   (this is the second square)........(2)
since the area of the second square is nine times the first, (it's the only given condition, so we start from that.)
$A_2=9A_1$
subbing (1) and (2) into it, we get,
$l_2^2=9l_1^2$|

what did you get after taking thesquare roots of both sides?

anonymous · Answer

sorry im back and thank you.

anonymous · Answer

Just take the square root both the sides and tell us what you got as @Shadowys said above..

anonymous · Answer

Getting ?? @Brianna9898

anonymous · Answer

I have no idea!

anonymous · Answer

Are you getting till here"

$$l_2^2=9 l_1^2$$

anonymous · Answer

why is there a 1 & 2 at the bottom

anonymous · Answer

See when you will take square root you will get like:

$$\large \sqrt{l_2^2} = \sqrt{9 l_1^2}$$

Can you tell what is this:
$$\large \sqrt{l_2^2} = ??$$

anonymous · Answer

... and how am I supposed to square root an l ??

anonymous · Answer

Oh that..

$l_1$ is showing length of first square.
$l_2$ is for length of second square.

anonymous · Answer

you can actually..

See,
What is square root of this:
$$\large \sqrt{2^2} = ??$$

anonymous · Answer

2

anonymous · Answer

Similar way what will be square root of this:
$$\large \sqrt{l_2^2} = ??$$

anonymous · Answer

$$l$$

anonymous · Answer

??

anonymous · Answer

Or you can say $l_2$..

Good..

anonymous · Answer

Similarly can you tell for:

$$\large \sqrt{9l_1^2} = ??$$

anonymous · Answer

so you have to keep the 2 at the bottom

anonymous · Answer

the one and two are sub scripts to differentiate between the first length and the second, thus, 1 and 2 respectively.

anonymous · Answer

see, 1 and 2 is differentiating lengths of the two square you are given with, so don't think here of just l think here of $l_1$ and $l_2$..

anonymous · Answer

so it would be $$9l _{1} ??$$

anonymous · Answer

You forgot to take square root of 9.

\(l_1\0 is good though..

anonymous · Answer

What is square root of 9?

anonymous · Answer

3

anonymous · Answer

Yep after square root you will get like:

$$\large l_2 = 3 \times l_1$$

anonymous · Answer

So, which answer choice is this?

anonymous · Answer

the first one?

anonymous · Answer

Well Done...

anonymous · Answer

And give all the thanks to @Shadowys

anonymous · Answer

yayyy! thank you guys for helping me!

anonymous · Answer

I don't even know how to give a medal on this thing

anonymous · Answer

Are you seeing best response after shadows post ?/

Just click that..

anonymous · Answer

oh okay, can I give a medal to two ppl?

anonymous · Answer

No, just only one..

anonymous · Answer

On one post you can give medal to one only..

anonymous · Answer

thanx for the medal @Shadowys !