Question

the sum of areas of two squares is 400 and the difference of the perimeter is 16. find the length of the side

Answer 1

Let side of first square be x and the side of another square be y.
difference in perimeter of two squares:-
4x-4y=16
4(x-y)=16
x-y=16/4
therefore, x-y=4
and x=4+y---take this(1)
 
sum of areas of two squares:-
 x²+y²=400
Put (1) here
(4+y)²+y²=400
(4)²+(y)²+2×4×y+y²=400
16+y²+8y+y²=400
2y²+8y+16-400=0
2y²+8y-384=0
2(y²+4y-192)=0 (here we have taken 2 common and take to another side. then it becomes:-)
y²+4y-192=0
we have done with factorisation method:-
y²-12y+16y-192=0
y(y-12)+16(y-12)=0
(y+16) (y-12)=0
either:-                             |             or:-
y+16=0                            |                   y-12=0
y= -16                              |                   y=12

we will take y=12 because y being side cannot be negative.
So, y=12
put y=12 in (1)
x=4+y
x=4+12
therefore, x=16
and hence, Side of first square= x = 16
and Side of another square= y = 12

Answer 2

length of side is 12 and 16