TS EAMCET · Maths · Properties of Triangles
The lengths of the sides of a triangle are 13 , 14 and 15 . If \(R\) and \(r\) respectively denote circumradius and inradius of that triangle, then \(8 R+r=\)
- A 84
- B \(\frac{65}{8}\)
- C 4
- D 69
Answer & Solution
Correct Answer
(D) 69
Step-by-step Solution
Detailed explanation
Let \(a=13, b=14\) and \(c=15\). Then \[ S=\frac{a+b+c}{2}=\frac{13+14+15}{2}=21 \] and area of triangle, \[ \begin{aligned} \Delta & =\sqrt{s(s-a)(s-b)(s-c)} \\ & =\sqrt{21(21-13)(21-14)(21-15)} \\ & =\sqrt{21 \times 8 \times 7 \times 6}=7 \times 3 \times 4=84 \end{aligned} \]…
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