Question

If an angle of a triangle remains unchanged but each of its two including side is doubled, then by what factor does the area get multiplied ?

• A. 2
• B. 3
• C. 4
• D. 6

Answer 1

The Correct Option is C

Assume the area of the triangle be A.
A = \(\frac{1}{2}\) × b × c  × sin A (b, c are both the sides which have included angle A)
both the sides b, c are doubled and the side A remains same
A' (new area) = \(\frac{1}{2}\) × 2b × 2c × sinA 
A' = 2bcsinA 
= 4A
So the New Area becomes 4 times of previous area.
The correct option is (C)