Question 77

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

Solution

Let the 2 sides be $$a=b=2$$ cm each, and the angle between them be $$\theta$$

Now, area of triangle = $$\frac{1}{2} ab sin\theta$$

=> $$A=\frac{1}{2}\times2\times2\times sin\theta=2sin\theta$$ $$cm^2$$

When the sides are doubled, => $$a'=b'=4$$ cm

=> $$A'=\frac{1}{2}\times4\times4\times sin\theta=8sin\theta$$ $$cm^2$$

$$\therefore$$ $$\frac{A'}{A}=4$$

=> Ans - (C)

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