MCQ
In $\triangle\text{ABC},$ if $AB = 16cm, BC = 12cm$ and $AC = 20cm$, 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 $AB = 16cm, BC = 12cm$ and $AC = 20cm$
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 $AB = 16cm, BC = 12cm$ and $AC = 20cm$
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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