Question 65

Let ABC be an isosceles triangle. Suppose that the sides AB and AC are equal and let the length of AB be x cm. Let b denote the angle ∠ABC and sin b = 3/5. If the area of the triangle ABC is M square cm, then which of the following is true about M?

Solution

$$\triangle$$ ABC can be represented as shown above where AD $$\bot$$ BC

Given, Sin b = $$\frac{3}{5}$$

Hence, AD = $$\frac{3x}{5}$$ and BD = $$\frac{4x}{5}$$

Now, BC = 2 BD = $$\frac{8x}{5}$$

$$\therefore$$ area of $$\triangle$$ ABC = $$\frac{1}{2}$$ * BC * AD = $$\frac{1}{2}$$ * $$\frac{8x}{5}$$ * $$\frac{3x}{5}$$ = $$\frac{12x^{2}}{25}$$

Only option E satisfies.

Hence, option E.

Video Solution

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