MCQ
In a $\triangle\text{ABC},$ if $\angle\text{B} = \angle\text{C} = 45^\circ,$ which is the longest side?
- A$AC$
- BNone of these.
- ✓$BC$
- D$CA$
✓
Answer
Correct option: C.
$BC$
We know that sum of all angles of a triangle is $180^\circ \angle\text{A} + \angle\text{B} + \angle\text{C} = 180^\circ$
$\angle\text{B} = \angle\text{C} = 45^\circ$
$\angle\text{A} + 45^\circ + 45^\circ = 180^\circ$
$\angle\text{A} + 90^\circ = 180^\circ$
$\angle\text{A} = 180^\circ - 90^\circ$
$\angle\text{A} = 90^\circ$
So, angle A is the largest and the side opposite to the greatest angle is the longest so, side $BC$ is the longest.
$\angle\text{B} = \angle\text{C} = 45^\circ$
$\angle\text{A} + 45^\circ + 45^\circ = 180^\circ$
$\angle\text{A} + 90^\circ = 180^\circ$
$\angle\text{A} = 180^\circ - 90^\circ$
$\angle\text{A} = 90^\circ$
So, angle A is the largest and the side opposite to the greatest angle is the longest so, side $BC$ is the longest.
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