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

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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:

A = 79 $\displaystyle A = 79$

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

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

Insufficient information is given to answer the problem.

A = 116 $\displaystyle A = 116$

Correct answer:

A = 79 $\displaystyle A = 79$

Explanation:

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

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

Simplify and set P = 888 $\displaystyle P = 888$ :

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

$\displaystyle 6A + 6B= 888$

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

$\displaystyle A + B = 148$

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

$\displaystyle A + B = 148$

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

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

A = 79 $\displaystyle A = 79$

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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 A + B $\displaystyle A + B$ ?

Possible Answers:

$\displaystyle 33$

$26\frac{2}{5}$ $\displaystyle 26\frac{2}{5}$

$\displaystyle 22$

$16 \frac{1}{2}$ $\displaystyle 16 \frac{1}{2}$

$\displaystyle 44$

Correct answer:

$\displaystyle 22$

Explanation:

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

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

Simplify and set P = 132 $\displaystyle P = 132$ :

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

$\displaystyle 6A + 6B= 132$

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

$\displaystyle A + B = 22$

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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 3:2 $\displaystyle 3:2$ . Evaluate $\displaystyle B$ .

Possible Answers:

B = 40 $\displaystyle B = 40$

B = 72 $\displaystyle B = 72$

B = 60 $\displaystyle B = 60$

B = 48 $\displaystyle B = 48$

B = 100 $\displaystyle B = 100$

Correct answer:

B = 40 $\displaystyle B = 40$

Explanation:

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

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

Simplify and set P = 600 $\displaystyle P = 600$ :

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

$\displaystyle 6A + 6B= 600$

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

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

then

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

and we can substitute as follows:

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

$\displaystyle 9B + 6B= 600$

$\displaystyle 15B = 600$

B = 40 $\displaystyle B = 40$

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

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #581 : Geometry

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

Example Question #581 : Geometry

All PSAT Math Resources

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