Question

Radius of incircle of ∆ABC divides one of the sides into two parts of 6 cm and 8 cm. If

the radius is 4 cm find the length of the other two sides of the triangle.​

Answer 1

Answer:

your answer is in the attachment

hope it helps you ♥️♥️

with regards @ARSH

Answer 2

Radius of the incircle of a ΔABC divides one of the sides into two parts of 6cm and 8cm. The radius is 4cm and the length of the other two sides of the triangle are 15 and 13 cm. The stepwise explaination is given below:

- The given circle touch the sides AB and AC of the triangle at point F and E respectively and the length of the line segment AF be x.

- In ABC,

CE = CD = 6cm (Tangents on the circle from point C)

- BF = BD = 8cm (Tangents on the circle from point B)

- AF = AE = x (Tangents on the circle from point A)

AB = AF + FB = x + 8

BC = BD + DC = 8 + 6 = 14

CA = CE + EA = 6 + x

- Perimeter of ΔABC

2s = AB + BC + CA

= x + 8 + 14 + 6 + x

= 28 + 2x

s = 14 + x

- Area of ΔOBC =1/2*b*h

=1/2*BC*4=2BC

- Area of ΔOCA =1/2*b*h

=1/2*CA*4=2CA

- Area of ΔOAB =1/2*b*h

=1/2*AB*4=2AB

- Area of ΔABC = Area of ΔOBC + Area of ΔOCA + Area of ΔOAB

=2BC + 2CA + 2AB

=2(14)+2(6+x)+2(x+8)

=28+12+2x+2x+16

=56+4x

- Either x+14 = 0 or x − 7 =0

Therefore, x = −14and 7

- However, x = −14 is not possible as the length of the sides will be negative.

Therefore, x = 7

- Hence, AB = x + 8 = 7 + 8 = 15 cm

CA = 6 + x = 6 + 7 = 13 cm