Fill $c a n / c a n n o t$ in the given blank.
We ________ construct $∆ A B C$ when $A C = 2.5 c m,$ $A B = 6 c m$ and $B C = 4.2 c m$

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Solution

For constructing a triangle, $t h e s u m o f l e n g t h s o f a n y t w o s i d e s o f a t r i a n g l e i s g r e a t e r t h a n t h e t h i r d s i d e .$
Step-1: Add sides $A C, A B$ and compare with $B C$
$A C + A B 2.5 + 6 8.5 c m$
$B C = 4.2 c m$
So, $A C + A B > B C$
Step-2: Add sides $A B, B C$ and compare with $A C$
$A B + B C 6 + 4.2 10.2 c m$
$A C = 2.5 c m,$
So, $A B + B C > A C$
Step-3: Add sides $A C, B C$ and compare with $A B$
$A C + B C 2.5 + 4.2 6.7 c m$
$A B = 6 c m$
So, $A C + B C > A B$
Here, $t h e s u m o f l e n g t h s o f a n y t w o s i d e s o f a t r i a n g l e i s g r e a t e r t h a n t h e t h i r d s i d e .$ in all three cases.
Hence, We $c a n$ construct $∆ A B C$ when $A C = 2.5 c m,$ $A B = 6 c m$ and $B C = 4.2 c m$

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