Question

Does anyone know how to solve this?

Answer 1

Setting the lengths of the lines equal to each other, we have:

`5x-4=4x+8`

`5x=4x+12`.

Isolating the x term, we get:

`x=12`.

Substituting
`x=12` back into the expressions for the lengths of the lines, we get:

`5x-4`

`5(12)-4`

`60-4`

`\boxed{56}`,

and

`4x+8`

`4(12)+8`

`48+8`

`\boxed{56}`.

So, the lengths of both lines are 56.

Note: We already know that both lines are congruent, so we don't need to substitute x=12 into both expressions.

Answer 2

Explanation:

To find the values of x that make these line segments congruent, you can set up an equation based on their lengths:5x - 4 = 4x + 8Now, solve for x:5x - 4x = 8 + 4

x = 12Now that you've found the value of x (which is 12), you can substitute it into either of the expressions to find the length of the congruent line segments AB and CD:For AB: AB = 5x - 4 = 5(12) - 4 = 60 - 4 = 56

For CD: CD = 4x + 8 = 4(12) + 8 = 48 + 8 = 56Both AB and CD have a length of 56 units since the line segments are congruent and have the same length.