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

Answer: (C)

4

Answer 2

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)