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Equal Angles Subtend Equal Sides

In a ABC, i...

Question

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

19

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17

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28

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Solution

The correct option is A $19$ cm
It is given that
$A B + B C = 10$ cm ....(i)
$B C + C A = 12$ cm ....(ii)
$C A + A B = 16$ cm ....(iii)
Adding (i), (ii) and (iii), we get
$2 (A B + B C + C A) = 10 + 12 + 16$
$\Rightarrow 2 (A B + B C + C A) = 38$
$\Rightarrow$ $A B + B C + C A = 19$ cm
Therefore, perimeter of $△ A B C$ is $19$ cm.

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