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Find the inradius of an equilateral triangle of side 10 cm user r = A/s |
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Answer» Side of equilateral triangle is a = 10 cm. ∴ s = semi perimeter of triangle \(=\frac{a+b+c}{2}=\frac{10+10+10}{2}\) = 30/2 = 15 cm And K = Area of equilateral triangle \(=\frac{\sqrt3}{4}a^2=\frac{\sqrt3}{4}\times10^2\) = 25√3 cm2 Now, inradius of the equilateral triangle is r = K/s \(=\frac{25\sqrt3}{15}=\frac{5\sqrt3}{3}\,cm.\) or inradius = r \(=\sqrt{\frac{(s-a)(s-b)(s-c)}{s}}\) \(=\sqrt{\frac{(15-10)(15-10)(15-10)}{15}}\) \(=\sqrt{\frac{5\times5\times5}{15}}=\sqrt{25/3}\) = 5/√3 = 5√3/3 cm |
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