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

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

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Example Questions

Example Question #41 : Geometry

Two sides of an isosceles triangle have lengths 3 feet and 4 feet. Which of the following could be the length of the third side?

Possible Answers:

\(\displaystyle 42 \textrm{ in}\)

\(\displaystyle 36 \textrm{ in}\)

\(\displaystyle 54 \textrm{ in}\)

\(\displaystyle 40 \textrm{ in}\)

\(\displaystyle 32 \textrm{ in}\)

Correct answer:

\(\displaystyle 36 \textrm{ in}\)

Explanation:

An isosceles triangle, by definition, has two sides of equal length. Having the third side measure either 3 feet or 4 feet would make the triangle meet this criterion.

3 feet is equal to \(\displaystyle 3 \times 12 = 36\) inches, and 4 feet is equal to \(\displaystyle 4 \times 12 = 48\) inches. We choose 36 inches, since that, but not 48 inches, is a choice.

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

The triangles are similar. Solve for \(\displaystyle x\).

Question_12

Possible Answers:

\(\displaystyle x=1\)

\(\displaystyle x=3\)

\(\displaystyle x=2\)

\(\displaystyle x=4\)

Correct answer:

\(\displaystyle x=2\)

Explanation:

Because the triangles are similar, proportions can be used to solve for the length of the side:

\(\displaystyle \frac{9}{3}=\frac{6}{x}\)

Cross-multiply:

\(\displaystyle 9x=18\)

\(\displaystyle x=2\)

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