Answer:
AB = 21
Step-by-step explanation:
Given:
AC = CE, with D as midpoint of CE,
CE = 10x + 18,
DE = 7x - 1,
BC = 9x + 2
Required:
Length of segment AB
SOLUTION:
Create an equation to enable you solve for the value of x
Since point D is the midpoint of CE, ½ of CE = DE.
Thus, we have the following equation:
½(10x + 18) = 7x - 1
Solve for x
Multiply both sides by 2
10x + 18 = (7x - 1)2
10x + 18 = 14x - 2
10x - 14x = -18 - 2
-4x = -20
Divide both sides by -4
x = 5
Find the numerical value of CE:
CE = 10x + 18
Plug in the value of x
CE = 10(5) + 18 = 50 + 18 = 68
Since AC = CE, therefore
AC = 68
BC = 9x + 2 = 9(5) + 2 = 45 + 2 = 47
AB + BC = AC
AB + 47 = 68 (substitution)
Subtract 47 from both sides
AB = 68 - 47
AB = 21