Segment an is the altitude to side bc in δabc. if ab = 3nc and an = 2nc, prove that ac = bn. (hint: use variables in such problems. let nc = x units and find the other lengths in terms of x.)

Answer :

The proof is as follows :

Step-by-step explanation:

Let NC = x

⇒ AB = 3x and AN = 2x

In Δ ABN, By using Pythagoras theorem,

AB² = BN² + AN²

⇒ BN² = AB² - AN²

⇒ BN² = (3x)² - (2x)²

⇒ BN² = 5x²

⇒ BN = x√5  .......................(1)

Now in ΔANC , Using Pythagoras theorem We have,

AC² = NC² + AN²

⇒ AC² = x² + (2x)²

⇒ AC² = 5x²

⇒ AC = x√5   ....................(2)

From equations (1) and (2) We get,

AC = BN , which is our required result

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