Question

question
triangle def is formed by connecting the mid - points of the side of triangle abc. the lengths of the sides of triangle abc are shown. find the perimeter of triangle def. figures not necessarily drawn to scale.
answer attempt 1 out of 2
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Explanation:

Step1: Recall mid - point theorem

The segment connecting the mid - points of two sides of a triangle is half the length of the third side of the triangle.

Step2: Find length of $DE$

Since $D$ and $E$ are mid - points of $AC$ and $BC$, $DE=\frac{1}{2}AB$. Given $AB = 10$, so $DE = 5$.

Step3: Find length of $EF$

Since $E$ and $F$ are mid - points of $BC$ and $AC$, $EF=\frac{1}{2}AB$. Given $AB = 10$, so $EF = 5$.

Step4: Find length of $DF$

Since $D$ and $F$ are mid - points of $AC$ and $AB$, $DF=\frac{1}{2}BC$. Given $BC = 16$, so $DF = 8$.

Step5: Calculate perimeter of $\triangle DEF$

Perimeter of $\triangle DEF=DE + EF+DF=5 + 6+8 = 19$.

Answer:

19