Question

Can someone please help me Find EF

Answer 1

Answer:

Step-by-step 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