Question

Given: DC =6x, and DA =4x+18 EB =4y-12, and ED =y+17 Y Find y. Then find ED, DB and EB.

Answer 1

Complete Question:

Given:

(1) DC = 6x, and DA = 4x + 18, find the value of x. Then find AD, DC, and AC

(2) EB = 4y - 12, and ED = y + 17. Find y. Then find ED, DB and EB.

Answer:

x = 9, AD = 54, DC = 54, AC = 108

y = 23, ED = 40, DB = 40, EB = 80

Step-by-step explanation:

The diagram for this question has been attached to this response.

(1) From the diagram, it can be observed that;

(a) DC and DA have equal lengths. i.e

=> DC = DA             ---------------------(i)                  

(b) AC = DA + DC    --------------------(ii)

But;

DC = 6x

DA = 4x + 18

Substitute the values of DC and DA into equation (i) as follows;

6x = 4x + 18          [Solve for x]

6x - 4x = 18

2x = 18

x = 9

Since x = 9, then

DC = 6x = 6(9) = 54

DA = 4x + 18 = 4(9) + 18 = 54

Therefore

DC = 54

AD = DA = 54

AC = 54 + 54 = 108       [using equation (ii)]

(2) Also, from the diagram, it can be observed that;

(a) ED and DB have equal lengths. i.e

=> ED = DB             ---------------------(iii)                  

(b) EB = ED + DB    --------------------(iv)

=>EB = ED + ED        [since ED = DB]

=>EB = 2ED             ------------------(v)

But;

EB = 4y - 12

ED = y + 17

Substitute the values of EB and ED into equation (v) as follows;

4y - 12 = 2(y + 17)          [Solve for y]

4y - 12 = 2y + 34

4y - 2y = 34 + 12

2y = 46

y = 46 / 2

y = 23

Since y = 23, then

EB = 4y - 12 = 4(23) - 12 = 80

ED = y + 17 = 23 + 17 = 40

Therefore

EB = 80

ED = DB = 40