Look! It's A Square!
1 2 + 1 2 + 1 2 + 1 2 + 2 2 + 2 2 + 2 2 + 3 2 = ?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
4 solutions
Yes! This is the intended solution. Thank you :)
1 2 + 1 2 + 1 2 + 1 2 + 2 2 + 2 2 + 2 2 + 3 2 = 4 × 1 2 + 3 × 2 2 + 9 = 2 5 = 5 □ 2
Seeing the image,it can be answered in seconds!
why use multiplication Operator? in this Question we give only Add operator
Log in to reply
I used multiplication to make the solution easier, I guess. It's not a necessity though.
It's called factoring. There are 4 (1^2) terms, 3 (2^2) terms, and 1 (3^2) term, so it can be rewritten as such.
It should read 4(1)^2, not 3(1)^2.
1 2 + 1 2 + 1 2 + 1 2 + 2 2 + 2 2 + 2 2 + 3 2 = 2 ( 2 × 1 2 ) + 2 × 2 2 + 2 2 + 3 2 = 2 2 + 2 ( 2 × 1 2 + 2 2 ) + 3 2 = 2 2 + 2 ( 2 ) ( 1 2 + 2 ) + 3 2 = 2 2 + 2 ( 2 ) ( 3 ) + 3 2 = ( 3 + 2 ) 2 = 5 2 = 2 5
The image is extremely helpful in visualizing what's happening. The side length of the biggest inner square is 3 and the next largest inner square's side length is 2. This means the base of the entire square is 5. The area of a square is, not incidentally, the side length squared. So, the answer is 5^2.
More algebraically, you have 4(1)^2 + 3(2)^2 + 3^2 = 4+12+9 = 25 = 5^2