MCQ
In $\triangle\text{ABC},$ if $AB = 16\ cm, BC = 12\ cm$ and $AC = 20\ cm,$ then $\triangle\text{ABC}$ is :
- AAcute $-$ angled.
- ✓Right $-$ angled.
- CObtuse $-$ angled.
- DNot possible.
✓
Answer
Correct option: B.
Right $-$ angled.
Note that first check if the sum of any two sides is greater than the third side.
Since in this triangle, it holds, a triangle is possible.
In $\triangle\text{ABC},$
if $AB = 16\ cm, BC = 12\ cm$ and $AC = 20\ cm$
Consider,
$A B^2+B C^2=16^2+12^2=400$
$A C^2=20^2=400 $
By the Converse of Pythagoras theorem,
$\triangle\text{ABC}$ will be a right $-$ angled triangle.
Since in this triangle, it holds, a triangle is possible.
In $\triangle\text{ABC},$
if $AB = 16\ cm, BC = 12\ cm$ and $AC = 20\ cm$
Consider,
$A B^2+B C^2=16^2+12^2=400$
$A C^2=20^2=400 $
By the Converse of Pythagoras theorem,
$\triangle\text{ABC}$ will be a right $-$ angled triangle.
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