Question

Y is between X and Z. Find the length of YZ if

XY = 3a - 4, YZ = 6a + 2, and XZ = 5a + 22.
(Line segments and distance)

Answer 1

The length of YZ is 38.

Since Y is between X and Z, we can use the following relationship:

XZ = XY + YZ

Substituting the given expressions, we get:

5a + 22 = (3a - 4) + (6a + 2)

Simplifying the equation, we get:

5a + 22 = 9a - 2

Combining like terms, we get:

4a = 24

Dividing both sides by 4, we get:

a = 6

Now, we can substitute the value of a into the expression for YZ:

YZ = 6a + 2

YZ = 6(6) + 2

YZ = 36 + 2

YZ = 38

Answer 2

`YZ=38\ units`

Explanation:

we know that

If Y is between X and Z

then

`XZ=XY+YZ`

substitute the given values and solve for a

(
`5a+22)=(3a-4)+(6a+2)\\(5a+22)=(9a-2)\\9a-5a=22+2\\4a=24\\a=6`

Find the length of YZ

`YZ=6a+2`

substitute the value of a

`YZ=6(6)+2=38\ units`