Question

In the given figure ABC is a triangular plot, OE = OF = OG = 2 cm. If the area of the plot is 40 cm2, then the semi-perimeter of the triangle ABC is
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Answer 1

Given : ABC is a triangular plot, OE = OF = OG = 2 cm

area of the plot is 40 cm²

To Find : the semi-perimeter of the triangle ABC

Solution:

Join OA , OB & OB

Area of Δ ABC = Area of ΔOAB + Area of ΔOBC + Area of ΔOAC

Area of ΔOAB  = (1/2) AB * OE  =  (1/2) AB * 2 =   AB    

Area of ΔOBC  = (1/2) BC * OF = (1/2) BC * 2 =   BC

Area of ΔOAC  = (1/2) AC * OG = (1/2) AC * 2 =   AC

Area of Δ ABC = AB + BC + AC

=> 40 = AB + BC + AC

Semi perimeter of Δ ABC =  = (AB + BC + AC)/2

= 40/2

= 20  cm

or Simply semi perimeter x inradius = Area of triangle

=> semi perimeter x 2 = 40

=>  semi perimeter  = 20 cm

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