Question

if $\triangle lafcong\triangle now$, find the length of $overline{lf}$.
$\triangle lafcong\triangle now$

Explanation:

Step1: Set equal corresponding sides

Since $\triangle LAF\cong\triangle NOW$, corresponding sides are equal. We can set $LF = NO$. So $4x=2x + 6$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides of the equation $4x=2x + 6$.
$4x-2x=2x + 6-2x$, which simplifies to $2x=6$. Then divide both sides by 2: $\frac{2x}{2}=\frac{6}{2}$, so $x = 3$.

Step3: Find the length of $LF$

Substitute $x = 3$ into the expression for $LF$. Since $LF=4x$, then $LF=4\times3=12$.

Answer:

$12$