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.

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.

Answers to choose from:

 

A. 9
B. 13.5
C. 27

Answer 1

Cody,

 

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. 

 

Hope it helps.

 

Heng