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Question 26

In a triangle with integer side lengths, one side is thrice the other. The third side is 15 cm. The greatest possible perimeter of the triangle is in cm


Correct Answer: 43

Solution

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Let the two related sides be $$x$$ and $$3x$$, with the third side $$15$$. The triangle inequalities give $$3x-x<15$$ and $$3x+x>15$$, so $$\frac{15}{4}<x<\frac{15}{2}$$. The greatest integer value is $$x=7$$, giving perimeter $$7+21+15=43$$.

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