Question

if $lkcong mk$, $lk = 7x - 10$, $kn=x + 3$, $mn=9x - 11$, and $kj = 28$, find $lj$.

Explanation:

Step1: Use the congruence of line - segments

Since $\overline{LK}\cong\overline{MK}$, we have $LK = MK$. Given $LK = 7x - 10$ and $MK=MN - KN$. Also, $KN=x + 3$ and $MN = 9x-11$. So $MK=(9x - 11)-(x + 3)=9x-11-x - 3=8x-14$. Then set up the equation $7x - 10=8x - 14$.

Step2: Solve the equation for $x$

Subtract $7x$ from both sides of the equation $7x - 10=8x - 14$: $-10=x - 14$. Then add 14 to both sides, we get $x = 4$.

Step3: Find the length of $LK$

Substitute $x = 4$ into the expression for $LK$. $LK=7x - 10=7\times4-10=28 - 10 = 18$.

Step4: Calculate $LJ$

Since $LJ=LK + KJ$, and $KJ = 28$ and $LK = 18$, then $LJ=18 + 28=46$.

Answer:

46