Question

Sally has a polygon that is proportional to Jack's polygon, but hers has nine times as much area as his. How much larger are the sides of sally's polygon?

Answer 1

`ls=3l_(J)`

Explanation:

Let Sally's polygon be for example a square (As) where the area is equal to the square side and Jack (Aj) has a proportional one but Sally's is nine times larger than the Jack, then:

`As=9A_(J)\\A_(J)=l^(2)_(J)\\As=9A_(J)\\As=l^(2)s\\replacing\\l^(2)s=9A_(J)\\l^(2)s=9l^(2)_(J)\\\sqrt{l^(2)s}=\sqrt{9l^(2)_(J)}\\ls=3l_(J)`