Question

PLEASE HELP ASAP!!!!!! Thanks!!
What is the length of the base of an isosceles triangle if the center of the inscribed circle divides the altitude to the base into the ratio of 12:5 (from the vertex to the base), and the length of a leg is 60 cm?

Answer 1

Answer:

50 cm

Step-by-step explanation:

the center of the inscribed circle divides the altitude to the base into the ratio of 12:5

Let say Vertex to Center  = 12x  cm

Center to Base = 5x  cm

Radius = 5x cm

Altitude = 12x + 5x = 17x  cm

Area of Triangle =  (1/2) Base * Altitude

= (1/2) Base * 17x

Radius = 5x cm is altitude to all the three sides

so sum of area of three triangle formed = Area of triangle

Other two sides = 60 cm

= (1/2)Base * 5x + (1/2)*60 * 5x  +  (1/2)*60 * 5x  =   (1/2) Base * 17x

=> 60 * 5x =  Base * 6x

=> Base = 50 cm