Question

in the diagram below, line AB bisects CD at point E. If CD = 13x-15 and EC=5x+9, find the length of EC and the length of CD

Answer 1

EC = 64

CD = 128

Explanation:

AB bisects CD at E. So, EC = ED

EC + ED = CD

EC + EC = CD

2*(EC) = CD

2* (5x + 9) = 13x - 15

2*5x + 2*9 = 13x - 15

10x + 18 = 13x - 15

Subtract 10x from both sides

18 = 13x - 10x - 15

18 = 3x - 15

Add 15 to both sides

18 + 15 = 3x

33 = 3x

3x = 33

Divide both sides by 3

x =33/3

x = 11

Length of EC = 5x + 9 = 5*11 + 9 = 55 + 9 = 64

CD = 13x - 15 = 13*11 - 15 = 143 - 15 = 128