Question
What is the inradius of a right-angled triangle if its base
measures 20 cm and its height (perpendicular) is 21 cm?Solution
By Pythagoras theorem,
Hypotenuse 2 Â = base 2 Â + perpendicular 2
Hypotenuse 2 Â = 20 2 Â + 21 2
Hypotenuse 2 Â = 400 + 441 = 841
So, hypotenuse = 29 or – 29
But hypotenuse cannot be negative. So, hypotenuse = 29 cm
Inradius of a right-angled triangle = (Perpendicular + Base – Hypotenuse) ÷ 2 = (21 + 20 – 29) ÷ 2 = 6 cm
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