Question

The sum of the areas of two squares is 640 m . If the difference in their perimeter is 64m .Find the sides of the two squares

Answer 1

Answer:

The sides are 24cm,8cm

Step-by-step :

let a be the length of side of first square

area of 1st square = a^2

perimeter of 1st square = 4a

let b be the length of side of second square

area of 2nd square = b^2

perimeter of 2nd square = 4b

now

a^2+b^2 = 640 ............(1)

4a - 4b = 64

=> a - b = 16 ................(2)

(a-b)^2 = a^2 + b^2 - 2ab

=> 256 = 640 - 2ab

=> ab = 192

(a + b)^2 = a^2+b^2 + 2ab

(a+b)^2 = 640 + 384 = 1024

=> a + b = 32 .......................(3)

adding (2)+(3)

2a = 48

=> a = 24

put a value in equation (3)

24 + b = 3232

b = 8

therefore the lengths of sides of squares are 24 , 8

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