How to find the length of the side of an acute / obtuse isosceles triangle - ISEE Upper Level Mathematics Achievement
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Question
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?
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?
Answer
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 
inches, and 4 feet is equal to 
inches. We choose 36 inches, since that, but not 48 inches, is a choice.
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
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Question
The triangles are similar. Solve for 
.
The triangles are similar. Solve for
Answer
Because the triangles are similar, proportions can be used to solve for the length of the side:
Cross-multiply:
Because the triangles are similar, proportions can be used to solve for the length of the side:
Cross-multiply:
Compare your answer with the correct one above
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