Answer:
x = 6; length of line segment AD = 104
Step-by-step explanation:
2.
The two mini lines that cross line segment AB and line segment BD mean that line segment AB and line segment BD are congruent, or the same length.
So length of line segment AB = length of line segment BD.
The problem tells us that the length of line segment AB is 7x + 10, and the length of the line segment BD is 9x - 2.
We can set these equal to each other because we know they are equal.
length of line segment AB = length of line segment BD
7x + 10 = 9x - 2
Now you solve for x:
7x + 10 = 9x - 2
Add 2 to both sides:
7x + 12 = 9x
Subtract 7x from both sides:
12 = 2x
Divide both sides by 2:
6 = x
So the value of x is 6.
Now, we need to find the length of AD, which is just the two line segment lengths added together.
length of line segment AB + length of line segment BD
(7x + 10) + (9x - 2)
7x + 9x + 10 - 2
16x + 8
Now substitute x = 6 into this expression:
16(6) + 8
96 + 8
104
So the length of AD is 104.
