Question

9. If LK MK, LK = 7x - 10, KN = x + 3, MN = 9x - 11, and KJ = 28, find LJ.

Answer 1

Answer:

$LJ = 46$

Step-by-step explanation:

Given:

$LK = MK$

$LK = 7x - 10$

$KN = x + 3$

$MN = 9x - 11$

$KJ = 28$

Required:

LJ

Solution:

Step 1: create an equation to find the value of x

Since we are given that LK = MK, and LK = 7x - 10, let's find the expression for MK to get an equation.

$MK + KN = MN$ (segment addition postulate)

$MK = MN - KN$ (Subtract KN from each side)

$MK = (9x - 11) - (x + 3)$ (subtitution)

$MK = 9x - 11 - x - 3$

$MK = 9x - x - 11 - 3$

$MK = 8x - 14$

LK = MK, therefore,

$7x - 10 = 8x - 14$

Subtract 8x from each side

$7x - 10 - 8x = 8x - 14 - 8x$

$-x - 10 = -14$

Add 10 to both sides of the equation

$-x - 10 + 10 = -14 + 10$

$-x = -4$

Divide both sides by -1

$x = 4$

Step 2: Find LJ

$LJ = LK + KJ$ (segment addition postulate)

$LJ = (7x - 10) + (28)$

Plug in the value of x

$LJ = 7(4) - 10 + 28$

$LJ = 28 - 10 + 28$

$LJ = 46$