Question

In the diagram below, A C ≅ C E , and D is the midpoint of CE. If CE = 10x+18, DE = 7x-1, and BC = 9x+2, find AB.

Answer 1

D is the midpoint of CE, so if you draw a line with those three points, it'll look like C-D-E.

Since DE = 7x-1, which also means CD = 7x-1.

CD + DE = CE, so (7x-1)+(7x-1) = 10x+18.

Therefore, x = 5 and CE = 68.

Since AC is congruent to CE, AC = 68.

Assuming the point B is somewhere between AC.

Since BC = 9x-2 and x = 5, which means BC = 43.

AC - BC = AB, so 68 - 43 = 25.

Therefore, AB = 25

Answer 2

AB = 21

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