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Difference between revisions of "2024 AMC 12B Problems/Problem 22"

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Note that this is a 4-5-6 triangle
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==Problem 22==
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Let <math>\triangle{ABC}</math> be a triangle with integer side lengths and the property that <math>\angle{B} = 2\angle{A}</math>. What is the least possible perimeter of such a triangle?
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<math>
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\textbf{(A) }13 \qquad
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\textbf{(B) }14 \qquad
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\textbf{(C) }15 \qquad
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\textbf{(D) }16 \qquad
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\textbf{(E) }17 \qquad
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</math>
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==Solution 1==
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We will use typical naming for the sides and angles of the triangle, that is <math>AB=</math>

Revision as of 03:30, 14 November 2024

Problem 22

Let $\triangle{ABC}$ be a triangle with integer side lengths and the property that $\angle{B} = 2\angle{A}$. What is the least possible perimeter of such a triangle?

$\textbf{(A) }13 \qquad \textbf{(B) }14 \qquad \textbf{(C) }15 \qquad \textbf{(D) }16 \qquad \textbf{(E) }17 \qquad$

Solution 1

We will use typical naming for the sides and angles of the triangle, that is $AB=$

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