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

Answer:

$ls=3l_{J}$

Step-by-step 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:

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