In a triangle ABC, if a: b: c = 3: 7: 8, then is equal to

JEE MainMathematicsModerate

In a triangle ABC, if a: b: c = 3: 7: 8, then $\frac{R}{r}$
is equal to

Show answer and solution

a = 3x, b = 7x, c = 8x

S = \frac{3x + 7x + 8x}{2} = 9x

\Delta = \sqrt{9x(6x)2x(x)} = 6\sqrt{3}x^{2}

R = \frac{abc}{4\Delta} = \frac{3 \times.7 \times.8x}{4.6\sqrt{3}x^{2}} = \frac{7x}{\sqrt{3}}

r = \frac{\Delta}{S} = \frac{6\sqrt{3}x^{2}}{9x} = \frac{2\sqrt{3}x}{3}

\frac{R}{r} = \frac{\left( \frac{7x}{\sqrt{3}} \right)}{\left( \frac{2\sqrt{3}x}{3} \right)} = \frac{7}{2}

Source: Grass-G / M-24 Mathematics Paper 31 Dec.docx

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