The length of each side of a square is 3 in. more than the length of each side of a smaller square. the sum of the areas of the squares is 4545 in squared. in2. find the lengths of the sides of the two squares.

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