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ISEE Upper Level Math : How to find the length of the side of an acute / obtuse triangle

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Example Question #1 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

Which of the following could be the lengths of the three sides of a scalene triangle?

Possible Answers:

$3 \textrm{ ft, }36 \textrm{ in, }1\textrm{ yd}$ $\displaystyle 3 \textrm{ ft, }36 \textrm{ in, }1\textrm{ yd}$

$6 \textrm{ ft, }84 \textrm{ in, }5\textrm{ ft}$ $\displaystyle 6 \textrm{ ft, }84 \textrm{ in, }5\textrm{ ft}$

$5 \textrm{ ft, }66 \textrm{ in, }5 \frac{1}{2}\textrm{ ft}$ $\displaystyle 5 \textrm{ ft, }66 \textrm{ in, }5 \frac{1}{2}\textrm{ ft}$

$5 \textrm{ ft, }60 \textrm{ in, }4\textrm{ ft}$ $\displaystyle 5 \textrm{ ft, }60 \textrm{ in, }4\textrm{ ft}$

$7 \textrm{ ft, }84 \textrm{ in, }72\textrm{ in}$ $\displaystyle 7 \textrm{ ft, }84 \textrm{ in, }72\textrm{ in}$

Correct answer:

$6 \textrm{ ft, }84 \textrm{ in, }5\textrm{ ft}$ $\displaystyle 6 \textrm{ ft, }84 \textrm{ in, }5\textrm{ ft}$

Explanation:

A scalene triangle, by definition, has three sides of different lengths. We can identify the scalene triangle by converting measures to the same unit. We will convert to inches in this case.

$5 \textrm{ ft, }60 \textrm{ in, }4\textrm{ ft}$ $\displaystyle 5 \textrm{ ft, }60 \textrm{ in, }4\textrm{ ft}$

5 feet = $5 \times 12 = 60$ $\displaystyle 5 \times 12 = 60$ inches. This triangle can be eliminated, since two sides have length 60 inches.

$7 \textrm{ ft, }84 \textrm{ in, }72\textrm{ in}$ $\displaystyle 7 \textrm{ ft, }84 \textrm{ in, }72\textrm{ in}$

7 feet = $7 \times 12 = 84$ $\displaystyle 7 \times 12 = 84$ inches. This triangle can be eliminated, since two sides have length 84 inches.

$3 \textrm{ ft, }36 \textrm{ in, }1\textrm{ yd}$ $\displaystyle 3 \textrm{ ft, }36 \textrm{ in, }1\textrm{ yd}$

These three measures are equal. This is an equilateral triangle, and it can be eliminated.

$5 \textrm{ ft, }66 \textrm{ in, }5 \frac{1}{2}\textrm{ ft}$ $\displaystyle 5 \textrm{ ft, }66 \textrm{ in, }5 \frac{1}{2}\textrm{ ft}$

$5 \frac{1}{2}$ $\displaystyle 5 \frac{1}{2}$ feet = $5 \frac{1}{2} \times 12 = 66$ $\displaystyle 5 \frac{1}{2} \times 12 = 66$ inches. This triangle can be eliminated, since two sides have length 66 inches.

$6 \textrm{ ft, }84 \textrm{ in, }5\textrm{ ft}$ $\displaystyle 6 \textrm{ ft, }84 \textrm{ in, }5\textrm{ ft}$

5 feet = 60 inches.

6 feet = $6\times 12 = 72$ $\displaystyle 6\times 12 = 72$ inches.

The sides of this triangle measure 60, 72, and 84 inches, so the triangle is scalene.

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ISEE Upper Level Math : How to find the length of the side of an acute / obtuse triangle

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

All ISEE Upper Level Math Resources

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Example Question #1 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

All ISEE Upper Level Math Resources

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