In a $Δ$ $A B C$ , if $A B$ $+$ $B C$ $= 10$ cm, $B C$ $+$ $C A$ $= 12$ cm, $C A$ $+$ $A B$ $= 16$ cm, then the perimeter of the triangle is __________.

19

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17

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28

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22

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Solution

The correct option is B $19$ cm
Sides of the $Δ$ ABC are $A B, B C, C A$
Perimeter of triangle $Δ A B C = P = A B + B C + C A$
Given that
$A B + B C = 10$ cm ......(1)
$B C + C A = 12$ cm .....(2)
$A B + C A = 16$ cm ......(3)
Add above three equation, we get
$2 (A B + B C + C A) = 38$
$\Rightarrow 2 P = 38$
$\Rightarrow P = 19$ cm .....Perimeter

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