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ISEE Upper Level Quantitative : How to find the length of the side of a hexagon

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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All ISEE Upper Level Quantitative Resources

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Example Questions

Example Question #94 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Right_triangle

A regular hexagon has the same perimeter as the above right triangle. What is the length of one side of the hexagon?

Possible Answers:

$10 \frac{1}{3}\textrm{ in}$ $\displaystyle 10 \frac{1}{3}\textrm{ in}$

The length cannot be determined from the information given.

$12 \frac{2}{5}\textrm{ in}$ $\displaystyle 12 \frac{2}{5}\textrm{ in}$

$18 \frac{2}{3} \textrm{ in}$ $\displaystyle 18 \frac{2}{3} \textrm{ in}$

$22 \frac{2}{5} \textrm{ in}$ $\displaystyle 22 \frac{2}{5} \textrm{ in}$

Correct answer:

$18 \frac{2}{3} \textrm{ in}$ $\displaystyle 18 \frac{2}{3} \textrm{ in}$

Explanation:

By the Pythagorean Theorem, the hypotenuse of the right triangle is

$\sqrt{14^{2}+48^{2}} = \sqrt{196+2,304} = \sqrt{2,500} = 50$ $\displaystyle \sqrt{14^{2}+48^{2}} = \sqrt{196+2,304} = \sqrt{2,500} = 50$ inches, making its perimeter

$\displaystyle 14 + 48 + 50 =112$ inches.

The regular hexagon, which has six sides of equal length, has the same perimeter, so each side measures

$112 \div 6 = 18 \frac{2}{3}$ $\displaystyle 112 \div 6 = 18 \frac{2}{3}$ inches.

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Example Question #101 : Plane Geometry

Right_triangle

A regular hexagon has the same perimeter as the above right triangle. What is the length of one side of the hexagon?

Possible Answers:

$10 \frac{1}{3}\textrm{ in}$ $\displaystyle 10 \frac{1}{3}\textrm{ in}$

$22 \frac{2}{5} \textrm{ in}$ $\displaystyle 22 \frac{2}{5} \textrm{ in}$

$12 \frac{2}{5}\textrm{ in}$ $\displaystyle 12 \frac{2}{5}\textrm{ in}$

The length cannot be determined from the information given.

$18 \frac{2}{3} \textrm{ in}$ $\displaystyle 18 \frac{2}{3} \textrm{ in}$

Correct answer:

$18 \frac{2}{3} \textrm{ in}$ $\displaystyle 18 \frac{2}{3} \textrm{ in}$

Explanation:

By the Pythagorean Theorem, the hypotenuse of the right triangle is

$\sqrt{14^{2}+48^{2}} = \sqrt{196+2,304} = \sqrt{2,500} = 50$ $\displaystyle \sqrt{14^{2}+48^{2}} = \sqrt{196+2,304} = \sqrt{2,500} = 50$ inches, making its perimeter

$\displaystyle 14 + 48 + 50 =112$ inches.

The regular hexagon, which has six sides of equal length, has the same perimeter, so each side measures

$112 \div 6 = 18 \frac{2}{3}$ $\displaystyle 112 \div 6 = 18 \frac{2}{3}$ inches.

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All ISEE Upper Level Quantitative Resources

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ISEE Upper Level Quantitative : How to find the length of the side of a hexagon

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #94 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #101 : Plane Geometry

All ISEE Upper Level Quantitative Resources

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