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
