Question

Could you help me please?
@mathmale

Answer 1

My hypothesis is that it resembles option A, however I'm not quite sure that's 100% accurate.

Answer 2

Obviously the length of a side of the larger square is greater than the length of a side of the smaller square. We need only determine the factor by which the larger is greater than the smaller (e. g., twice as long, 16 times as long, etc.).

You could let x=length of a side of the smaller square and y=length of a side of the larger square. If f is the factor in question, then y=f*x.

What is the area of the 1st (smaller) square? the area of the 2nd (larger) square?
How would you write an equation showing how these two areas are related?

Answer 3

Further detail: I am stuck because 4 x4 = 16. Therefore, I would think it's C. but the wording I guess throws me off when it mentions "16 times greater"..

Answer 4

The best way to do this is to make up some numbers, and see from there

Example. Let Square A be \(8m^2\). Now, since Square B is 16 times that, Square B is \(128m^2\)

Since we know the square has equal lengths, we can find those lengths by using the square root for each area. Do this for both areas, and see if the length for Square B is 2, 4, 8 or 16 times Square A

Answer 5

TL;DR, how many times \(\sqrt{128}\) is bigger than \(\sqrt{8}\). That will be your answer

Answer 6

y is greater than x as x and y are defined here. What is the area of the square of side length x? that of the square with side length y?

Answer 7

sqrt 128= 11.31
sqrt 8 = 2.828 , rounded 2.83

Answer 8

Difference?
The difference is 8.49 , thus is would be 8 times greater- correct?

Answer 9

So, \(11.31\div 2.828=?\)

Answer 10

Not difference, divide them. See how many times the length of the smaller one can fit to the length of the bigger one

Answer 11

:( Darn! Thanks!
4.01 , thus is would be 4 times greater!

Answer 12

Yup, thats it @lilia222 :D

Answer 13

But do you understand how I got the numbers 128 and 8, and why did we square root them?

Answer 14

Perfect, so my answer would be 4 times greater even though the example is different?

Answer 15

Yes, your explanations were very detailed, precise, and helpful! :)

Answer 16

You could change the numbers around, from 8 to 99 to 76 to 42, and the bigger square will ALWAYS have a length 4 times greater :)

Answer 17

No problem @lilia222.

Answer 18

Thank you ! :DD