Question

Given LP, LM = (3x + 1), MN = (4x –3), NP = (6x – 5), and LM =NP.

M
AN
What is the length of MP?

Answer 1

`MP = 12`

Explanation:

Given

`LM = (3x + 1), MN = (4x -3), NP = (6x - 5)`

`LM = NP`

Required

Find MP

We have:

`LM = NP`

This gives:

`3x + 1 = 6x - 5`

Collect like terms

`3x - 6x = -1-5`

`-3x = -6`

Solve for x

`x = 2`

MP is calculated as:

`MP = MN + NP`

`MP = 4x - 3 + 6x - 5`

Collect like terms

`MP = 4x + 6x - 3 - 5`

`MP = 10x - 8`

Substitute
`x=2`

`MP = 10*2 - 8`

`MP = 20 - 8`

`MP = 12`