How to find the length of the side of an acute / obtuse triangle - ISEE Upper Level Quantitative Reasoning

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Question

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

Answer

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.

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

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

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

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

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

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

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

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

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

5 feet = 60 inches.

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

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

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Question

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

Answer

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.

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

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

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

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

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

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

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

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

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

5 feet = 60 inches.

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

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

Compare your answer with the correct one above

Question

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

Answer

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.

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

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

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

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

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

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

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

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

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

5 feet = 60 inches.

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

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

Compare your answer with the correct one above

Question

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

Answer

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.

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

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

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

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

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

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

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

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

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

5 feet = 60 inches.

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

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

Compare your answer with the correct one above

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