If an angle of a triangle remains unchanged but each of its two including sides is doubled, then by what factor does the area get multiplied ?
If an angle of a triangle remains unchanged but each of its two including sides is doubled, then by what factor does the area get multiplied ? Correct Answer 4
Original area = $$\frac{1}{2}ab\sin \theta $$New area :
$$\eqalign{ & = \frac{1}{2} \times \left( {2a} \right) \times \left( {2b} \right)\sin \theta \cr & = 4\left( {\frac{1}{2}ab\sin \theta } \right) \cr & = 4 \times {\text{ original area}} \cr} $$
