Circle c is inscribed in triangle jeg. what is the perimeter of triangle jeg? 60 units 65 units 70 units 75 units

60

I just took the test.

From the figure we get FG = GH (the tangent from a point G to a circle is equal)

Therefore 3x-5= 2x

                x=5

FG=5, GH =3x-5 = 10 (the tangent from a point G to a circle is equal)

JK=JH =x+5=10

EK = EF=x+5 =10 (the tangent from a point G to a circle is equal)

Therefor sides of triangle EGJ are  

EG=20, GJ=20 and EJ=20. EGJ is an equilateral triangle

So the perimeter of triangle =60 units

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x