Question

Sum of the areas of two square is 244cm.sq and the difference between their perimeter is 8cm Find the ratio of their diameter ​

Answer 1

Answer:

Step-by-step explanation:

Please recheck the question?

How can a square have a diameter?

Or this is the answer,

Let the sides of two square be x and y respectively.

So area of first sqaure = x²

And area of second square = y²

Given the sum of their squares is 244

=> x² + y² = 244...........(i)

Now perimeter of first sq. = 4x

and that of second = 4y

Given difference of their perimeter is 8

=> 4x - 4y = 8

=> 4(x - y) = 8

=> x - y = 8/4 = 2.............(ii)

Now squaring both sides in equation ii

(x - y)² = (2)²

=> x² + y² - 2xy = 4

Substituting value of x² + y² from eqn. (i)

we get

244 - 2xy = 4

=> -2xy = 4 - 244

=> -2xy = -240

=> 2xy = 240...............(iii)

Now in equation (i)

Adding 2xy on both sides,

x² + y² + 2xy = 244 + 2xy

Putting value of 2xy in R.H.S from eqn. (iii)

x² + y² + 2xy = 244 + 240

=> (x + y)² = 484

=> (x + y)² = (22)²

=> x + y = 22 .............(iv)

Now adding i and iv eqn.

x + y + x - y = 22 + 2

=> 2x = 24

=> x = 24/2 = 12

and hence, from eqn. iv

x + y = 22

=> 12 + y = 22

=> y = 22 - 12

=> y = 10

Thanks!!!