How to find the length of the side of a hexagon - PSAT Math

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Question

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above figure is 600. The ratio of to is . Evaluate .

Answer

The perimeter of the figure can be expressed in terms of the variables by adding:

Simplify and set :

Since the ratio of to is equivalent to - or

,

then

and we can substitute as follows:

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Question

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above figure is 132. What is ?

Answer

The perimeter of the figure can be expressed in terms of the variables by adding:

Simplify and set :

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Question

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above hexagon is 888. Also, . Evaluate .

Answer

The perimeter of the figure can be expressed in terms of the variables by adding:

Simplify and set :

Along with , we now have a system of equations to solve for by adding:

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