## Example Questions

### Example Question #1 : How To Find If Hexagons Are Similar

Two hexagons are similar. If they have the ratio of 4:5, and the side of the first hexagon is 16, what is the side of the second hexagon?      Explanation:

This type of problem can be solved through using the formula: If the ratio of the hexagons is 4:5, then and . denotes area. The side length of the first hexagon is 16.

Substituting in the numbers, the formula looks like: This quickly begins a problem where the second area can be solved for by rearranging all the given information.   The radical can then by simplified with or without a calculator.

Without a calculator, the 320 can be factored out and simplified:  ### Example Question #22 : Hexagons

The ratio between two similar hexagons is . The side length of the first hexagon is 12 and the second is 17. What must be?      Explanation:

This kind of problem can be solved for by using the formula: where the values are the similarity ratio and the values are the side lengths.

In this case, the problem provides , but not . is denoted as in the question.

There are four variables in this formula, and three of them are provided in the problem. This means that we can solve for ( ) by substituting in all known values and rearranging the formula so it's in terms of    ### All ACT Math Resources 