Question

The sides of a quadrilateral are 3, 4, 5, and 6. Find the length of the shortest side of a similar quadrilateral whose area is 9 times as great.

Answer 1

If you scale up area by 9, you scale up length by \[\sqrt{9}\] = 3.
So the shortest side = 3 * 3 = 9.

(Think of a square: if you double the length, you get a square with 4 x the area. It's the same with any other shape really, since you can chop it into tiny squares to approximate its area.)