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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Properties of Triangles

NTA Abhyas 2020 · Mathematics · Properties of Triangles

The inradius of the triangle having sides 26, 28, 30 units is

The inradius of the triangle having sides 26,28,3026, 28, 30 units is

Correct answer

8

Step-by-step solution

s=26+28+302=42s = \dfrac{26 + 28 + 30}{2} = 42
Δ=s(s−a)(s−b)(s−c)\Delta = \sqrt{s\left(s - a\right)\left(s - b\right)\left(s - c\right)}
=42(42−26)(42−28)(42−30)= \sqrt{42\left(42 - 26\right)\left(42 - 28\right)\left(42 - 30\right)}
=42×16×14×12= \sqrt{42 \times 16 \times 14 \times 12}
=(7×6)×(4×4)×(7×2)×(6×2)= \sqrt{\left(7 \times 6\right) \times \left(4 \times 4\right) \times \left(7 \times 2\right) \times \left(6 \times 2\right)}
=7×6×4×2= 7 \times 6 \times 4 \times 2
r=Δs=7×6×4×242=8r = \dfrac{\Delta}{s} = \dfrac{7 \times 6 \times 4 \times 2}{42} = 8
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