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

Side of smaller square= 3 inch and length of larger square = 6 inch 

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.

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