TS EAMCET · Maths · Properties of Triangles
If the sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the area (in sq. units) of that triangle is
- A 6
- B \(\frac{15}{4} \sqrt{7}\)
- C \(\frac{18}{5} \sqrt{7}\)
- D \(\frac{14}{3} \sqrt{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{15}{4} \sqrt{7}\)
Step-by-step Solution
Detailed explanation
Let three sides are \(x-1, x, x+1\). Given, largest angle is twice the smallest angle \(\begin{aligned} \therefore \quad \cos \theta & =\frac{(x+1)^2+(x)^2-(x-1)^2}{2 x(x+1)} \\ & =\frac{x^2+2 x+1+x^2-x^2+2 x-1}{2 x(x+1)} \end{aligned}\)…
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