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The sides of a triangle measure 4,6, and 7. If the shortest side of a similar triangle is 12, what is the perimeter of the larger triangle?

User Flash
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Given that both triangles are similar, then their corresponding sides satisfy a proportion.

The next relation must be satisfied:


(AB)/(DE)=(BC)/(EF)=(AC)/(DF)

Let's suppose that AB and DE are the shortest sides of each triangle, then:


\begin{gathered} (AB)/(DE)=(4)/(12)=(1)/(3) \\ or \\ 3AB=DE \end{gathered}

Also,


\begin{gathered} 3BC=EF \\ 3AC=DF \end{gathered}

The perimeter of the smaller triangle is,


\begin{gathered} P=AB+BC+AC \\ P=4+6+7 \\ P=17 \end{gathered}

The perimeter of the larger triangle is,


\begin{gathered} P=DE+EF+DF \\ P=3AB+3BC+3AC \\ P=3(AB+BC+AC) \end{gathered}

But, AB + BC + AC is the perimeter of the smaller triangle, which is 17, then the perimeter of the larger triangle is 3*17 = 51

The sides of a triangle measure 4,6, and 7. If the shortest side of a similar triangle-example-1
User Scarface
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