TS EAMCET · Maths · Properties of Triangles
Let ABC be a triangle right angled at B. If \(a=13\) and \(c=84\), then \(\mathrm{r}+\mathrm{R}=\)
- A \(42.5\)
- B \(169\)
- C \(98\)
- D \(48.5\)
Answer & Solution
Correct Answer
(D) \(48.5\)
Step-by-step Solution
Detailed explanation
\(b = \sqrt{a^2+c^2} = \sqrt{13^2+84^2} = \sqrt{169+7056} = \sqrt{7225} = 85\) \(R = \frac{b}{2} = \frac{85}{2} = 42.5\) \(r = \frac{a+c-b}{2} = \frac{13+84-85}{2} = \frac{12}{2} = 6\) \(r+R = 6+42.5 = 48.5\)
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