sum of areas of two squares is 400 CM square and difference of their perimeter is 16 cm find the side of two squares
Answers
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.