How to find the length of the side of an acute / obtuse isosceles triangle

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

Questions 1 - 2

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?

$36 \textrm{ in}$

$40 \textrm{ in}$

$42 \textrm{ in}$

$32 \textrm{ in}$

$54 \textrm{ in}$

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