Answer :
No, the quotient of two perfect squares is not always a perfect square. take 16/9 for example, it equals 1.77777777(bar notation), which is most certainly not a perfect square.
AND
If the area of the smaller square is 256, then its side length is 16. Putting 16 into the ratio, the new ration would be 16:36 because both the 4 and 9 are multiplied by 4. So, the side length of the larger triangle is 36.
AND
If the area of the smaller square is 256, then its side length is 16. Putting 16 into the ratio, the new ration would be 16:36 because both the 4 and 9 are multiplied by 4. So, the side length of the larger triangle is 36.