In , if AB = 16 cm, BC = 12 cm and AC = 20 cm, then is: - Vidyadip

MCQ

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

A
Acute$-$angled.
✓
Right$-$angled.
C
Obtuse$-$angled.
D
Not 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,
$AB^2+BC^2=16^2+12^2=400$
$AC^2=20^2=400$
By the Converse of Pythagoras theorem,
$\triangle\text{ABC}$ will be a right$-$angled triangle.

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