Question

what is the length of ln, when m is the mid - point of ln? 5x - 7 3(x + 7) l m n 126 63 28 14

Explanation:

Step1: Set up equation

Since M is the mid - point of LN, then LM = MN. So, $5x−7 = 3(x + 7)$.

Step2: Expand right - hand side

Expand $3(x + 7)$ to get $3x+21$. The equation becomes $5x−7=3x + 21$.

Step3: Solve for x

Subtract $3x$ from both sides: $5x-3x−7=3x-3x + 21$, which simplifies to $2x−7 = 21$. Then add 7 to both sides: $2x-7 + 7=21 + 7$, so $2x=28$. Divide both sides by 2: $x = 14$.

Step4: Find length of LM or MN

Substitute $x = 14$ into the expression for LM: $LM=5x−7=5\times14−7=70 - 7=63$.

Step5: Find length of LN

Since $LN=LM + MN$ and $LM = MN = 63$, then $LN=63+63 = 126$.

Answer:

126