Let the length of the smaller square= x
Then length of larger square= x+3
Sum of areas of both squares= 45 square in.
So equation is:
x²+(x+3)²=45
Expand
x²+x²+9+6x=45
2x²+6x-36=0
Factor out 2.
2(x²+3x-18)=0
x²+3x-18=0
Factorise
x²+6x-3x-18=0
x(x+6)-3(x+6)=0
(x-3)(x+6)=0
Using zero factor theorem:
x-3=0 or x=3
and x+6=0 or x=-6
Take positive value.
So length of side of smaller square= 3 in
And length of larger square= 3 + 3 = 6 in
Answer: Side of smaller square= 3 inch and length of larger square = 6 inch