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.
a) 9
b) 13.5
c) 27

When a shape's area is 9 times as great, the one dimension difference is  √9=3 times as great. therefore the length of all sides are 3 times of the corresponding sides of the original shape. the shortest side in the original shape is 3, the larger one is 3 times of that, which is 9.  general rule, if a similar shape is x times ratio in terms of sides, the area will be x^2 times the original.

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