Answer:
Explanation:
Remark
The relationship that solves this is
The outside segment * the whole length of the secant = the outside segment of the other secant * the whole length of the second secant.
Put in symbolic (and hence easier language)
GF * EG = HG * SG
Givens
GF = 4
EG = 2x + 4
GH = 5
SG = x + 5
Equation
4*(2x + 4) = 5*(x + 5) Remove the brackets
8x + 16 = 5x + 25 Subtract 5x from both sides
8x - 5x + 16 = 25 Combine
3x + 16 = 25 Subtract 16 from both sides
3x = 25 - 16
3x = 9 Divide by 3
3x/3 = 9/3
x = 3
EF = 2 * 3
EF = 6