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 sq. cm, then which of the following is true about M?
Explanation:
Now ∆ABC is an isosceles triangle where AB = AC. Let a perpendicular from A meet BC at D. As ∆ABC is isosceles, AD is a perpendicular bisector and BD = CD.
Given, Sin b = 3/5
⇒ Cos b = 4/5
In ∆ABD,
Sin b = 35 = ADAB
⇒ AD = 35AB = 3x5
Also, Cos b = 45 = BDAB
BD = 45AB = 4x5
∆ABC, BD = CD = 4x/5
∴ BC = 8x/5
⇒ Area of ∆ABC = ½ × BC × AD = ½ × 8x/5 × 3x/5 = 12x/25 = 0.48x.
Looking at the options we can see that M lies between x2/4 and x2/2.
Hence, option (a).
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