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

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #581 : Geometry

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above hexagon is 888. Also, \displaystyle A-B = 10. Evaluate \displaystyle A.

Possible Answers:

\displaystyle A = 79

\displaystyle A = 93\frac{4}{5}

\displaystyle A = 60\frac{1}{2}

Insufficient information is given to answer the problem.

\displaystyle A = 116

Correct answer:

\displaystyle A = 79

Explanation:

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

\displaystyle A + B + A + B + \left (2A + 2B \right ) + \left (2A + 2B \right ) = P

Simplify and set \displaystyle P = 888:

\displaystyle A + A + 2A + 2A + B+ B +2B + 2B= 888

\displaystyle 6A + 6B= 888

\displaystyle 6\left (A + B \right )= 888

\displaystyle A + B = 148

Along with \displaystyle A-B = 10, we now have a system of equations to solve for \displaystyle A by adding:

\displaystyle A + B = 148

\displaystyle \underline{A-B =\; 10}

\displaystyle 2A = \; \; \; \; \; \; 158

\displaystyle A = 79

 

Example Question #1 : How To Find The Length Of The Side Of A Hexagon

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above figure is 132. What is \displaystyle A + B ?

Possible Answers:

\displaystyle 33

\displaystyle 26\frac{2}{5}

\displaystyle 22

\displaystyle 16 \frac{1}{2}

\displaystyle 44

Correct answer:

\displaystyle 22

Explanation:

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

\displaystyle A + B + A + B + \left (2A + 2B \right ) + \left (2A + 2B \right ) = P

Simplify and set \displaystyle P = 132:

\displaystyle A + A + 2A + 2A + B+ B +2B + 2B= 132

\displaystyle 6A + 6B= 132

\displaystyle 6\left (A + B \right )= 132

\displaystyle A + B = 22

Example Question #581 : Geometry

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above figure is 600. The ratio of \displaystyle A to \displaystyle B is \displaystyle 3:2. Evaluate \displaystyle B

Possible Answers:

\displaystyle B = 40

\displaystyle B = 72

\displaystyle B = 60

\displaystyle B = 48

\displaystyle B = 100

Correct answer:

\displaystyle B = 40

Explanation:

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

\displaystyle A + B + A + B + \left (2A + 2B \right ) + \left (2A + 2B \right ) = P

Simplify and set \displaystyle P = 600:

\displaystyle A + A + 2A + 2A + B+ B +2B + 2B= 600

\displaystyle 6A + 6B= 600

Since the ratio of \displaystyle A to \displaystyle B is equivalent to \displaystyle 3:2 - or

\displaystyle \frac{A}{B} = \frac{3}{2},

then 

\displaystyle A = \frac{3}{2} B

and we can substitute as follows:

\displaystyle 6 \cdot \frac{3}{2}B + 6B= 600

\displaystyle 9B + 6B= 600

\displaystyle 15B = 600

\displaystyle B = 40

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