Question

43. Tom and Jerry were playing mathematical puzzles
with each other. Jerry drew a square of sides 32 cm
and then kept on drawing squares inside the squares
by joining the mid points of the squares. She con-
tinued this process indefinitely. Jerry asked Tom to
determine the sum of the areas of all the squares
that she drew. Il Tom answered correctly then what
would be his answer?
(a) 2018
(b) 1021
To 512
(d) 1096​

Answer 1

Answer:

How can we find the ans . You didn't write the no of squares . But to find the area with no of squares is easy . You have to find the area of a square with side 32 cm which is 32×32 = 1024 cm sq and then multiply 1024 cm sq to the no of squares he has drawn .

Answer 2

Answer:

2048

Step-by-step explanation:

Given :

Jerry drew a square of side 32 cm  and then kept on drawing squares inside the squares  by joining the mid points of the squares. She continued this process indefinitely.

To find :

the sum of the areas of all the squares  that she drew.

Formula :

Area of the square = side × side = diagonal²/2

Solution :

The side of the first square is 32 cm

Area of the square = 32 cm × 32 cm = 1024 cm²

The second square, we get by joining the mid points of the first square.

the diagonal of the second square = side of the first square

 d = 32 cm

Area of the second square = 32²/2 = 1024/2 = 512 cm²

Similarly, we get the third square by joining the mid points of the second square.

the area of the third square = half the area of second square

      = 512/2 = 256 cm²

We get infinite squares by continuing the process.

The sequence of the areas of the squares is as follows :

1024 , 512 , 256 , ... ... ... ∞

The sequence is in Geometric Progression (GP) since we get each succeeding term by multiplying the preceding term with a constant.

Here, the constant is called constant ratio. (ratio of the succeeding term to the preceding term)

For the sequence we got,

 common ratio, r = 512/1024 = 1/2

 first term, a = 1024

We require the sum of the infinite terms of the sequence.

i.e., 1024 + 512 + 256 + ...

The sum of infinite terms of geometric progression is given by,

$\boxed{\sf S_{\infty}=\dfrac{a}{1-r} }$

Substituting the values,

$\sf S_{\infty}=\dfrac{1024}{1-\dfrac{1}{2}} \\\\ \sf S_{\infty}=\dfrac{1024}{\dfrac{1}{2}} \\\\ \sf S_{\infty}=1024 \times 2 \\\\ \sf S_{\infty}=2048$

Therefore, the required answer is 2048.