In a $Δ A B C, D$ and $E$ are respectively the mid-points of sides AB and AC. If AD = 3 cm, DE = 5 cm and AE = 3.5 cm, then the perimeter of $Δ A B C$ is equal to

11.5 cm

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22 cm

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23 cm

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26 cm

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Solution

The correct option is C 23 cm
In $Δ A B C, D$ and E are mid-points of AB and AC respectively.

So, DE||BC
$∴ \frac{A D}{A B} = \frac{D E}{B C}$
$\Rightarrow \frac{A D}{2 A D} = \frac{5}{B C}$
$\Rightarrow B C = 10 c m$
Perimeter of $Δ A B C = A B + B C + A C$
$= 2 A D + B C + 2 A E$
$= 2 \times 3 + 10 + 2 \times 3.5$
$= 6 + 10 + 7$
$= 23 c m$
Hence, the correct answer is option(3).

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