Question

A square of side length 64 cm is given. A second square
is obtained by connecting the mid-points of the sides of
the first square. If process of forming smaller inner
squares by connecting the mid-points of the sides of
the previous squares is continued, what will be the side
length of the eleventh square, counting the original
square as the first square ?​

Answer 1

Answer:

32

Step-by-step explanation:

Answer 2

Answer:

3$\sqrt{3}$/2$\sqrt{2}$

Step-by-step explanation:

The area of the first square is 4096.Calculating the area of the next square-

Calculate the area of the corner triangle.Base of triangle=32,perpendicular of triangle=32,and by PGT,the third side,ie. the side of the next square=$\sqrt{32^2+32^2}$=$\sqrt{2048}$.Therefore,the area of the 2nd square will be 2048sq.cm.

Similarly,the area will keep getting halved with the formation of each square.So,the resultant progression of areas of the squares(starting from the 1st)=

4096,2048,1024,512,216,108,54,27,13.5,6.25,3.125

As we can see clearly,the 11th square's area=3.125sq.cm or 27/8sq.cm.

Calculating the side=> $\sqrt{27/8} = 3\sqrt{3}/2\sqrt{2}$

This is the final answer.

I'd appreciate it if you thank me and mark it as the brainliest answer,it took me a lot of time to solve and write this question :)