By using the formula here are the answers:
Top row: A - 117mm B - 103mm C - 233mm
Bottom row: A - 202mm B - 57mm C - 232mm
here is the work
Top row A: 10^2 + 6^2 = x^2 136 =x^2, or sqrt136 cm = 11.66 cm=116.6 mm=117 mm by rounding
Top row B: 9^2+5^2 = x^2 106=x^2 or sqrt106=x = 10.3cm = 103mm
Top row C: 20^2+12^2=x^2 = 544=x^2=sqrt544 = x = 23.3cm=x = 233mm
Bottom row A: 23^2=11^2+x^2 = 529=121+x^2 = x^2=408 = sqrt408=x = 20.2cm = 202mm
Bottom row B: 9^2=7^2+x^2 = 81 = 49+x^2 = x^2=32 = sqrt32=x = 5.7cm = 57mm
Bottom row C: 30^2=19^2+x^2 = 900=361+x^2 = 539=x^2 = sqrt539 = x = 23.2 cm or 232mm
Hope this helps :)
3364. If we simply this problem to the differnce between 4^2 and 6^2, we see that the differnce is 20. This is basically eaual to the distance between 4^2 and 5^2 plus the distance between 5^2 and 6^2. To calculate the distance I use the formula (sq number, in this example 6 x 2-1), this means the distance from 5^2 to 6^2 is 11, and the distance from 4^2 to 5^2 is 9. We can also takeaway that the differenmce between squares is ALWAYS 2 greater than the last one.
So, back to the problem, we can tell that the squares have to be 113 and 115 apart, which means that 2x-1=115, meaning that x = 58, doing the same thing to 113, means that x = 56.
To check our answers, 58^2 is 3364, and 56^2 is 3136, the difference between these two is 228, meaning that our answer (58^2 or 3364) is correct!