Question

In a right triangle ABC, right angled at B, BC=12cm and AB=5cm. The radius of the circle inscribed in the triangle is

Answer 1

this will be the image of the triangle
as we know the radius of a circle inscribed in a right triangle is perpendicular to the sides (sorry as it is not so much accurate in the figure but the radius of the circle is perpendicular to all the sides)

Area of ABC = 1/2* 5*12 = 30. ------(I)
Also,
Area of ABC = 1/2*5*r + 1/2*12*r + 1/2*13*r
= 1/2*r*(5+12+13)
=1/2*r*30
= 15*r ---------(II)
(where r is radius of circle)
From I and II,
30= 15*r
=> r = 2 cm
hope it helps
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Answer 2

b=90

bc=12

ab=5

ac²=ab²+bc²

  =25+144=169

ac=√169=13 cm

diameter of circle = ab+bc-ac

= (12+5)-13 =4

diameter =4

2r=4

radius=4/2=2 cm