Sum of the areas of two squares is 400cm^2.if the difference of there perimeter is 16cm. Find the sides of the two squares?
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let side of first square x
side of second square y
x^2+y^2=400...... (2)
their perimeter 4x,4y
so 4x-4y=16 or x-y=4... (1)
so from (2)
(x-y)^2+2xy=400
or 16+2xy=400
or 2xy=384
or xy=192
so now (x+y)^2=(x-y)^2+4xy=4^2+4*192=16+768=784
so x+y=root 784=28
and x-y=4
so 2x=32 or x=16
y=12
so first square sides are 16 cms each
second square sides are 12 cms each
side of second square y
x^2+y^2=400...... (2)
their perimeter 4x,4y
so 4x-4y=16 or x-y=4... (1)
so from (2)
(x-y)^2+2xy=400
or 16+2xy=400
or 2xy=384
or xy=192
so now (x+y)^2=(x-y)^2+4xy=4^2+4*192=16+768=784
so x+y=root 784=28
and x-y=4
so 2x=32 or x=16
y=12
so first square sides are 16 cms each
second square sides are 12 cms each
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