In Δ ABC, ∠ C = 90º and Q is the midpoint of BC. If AB = 10 cm and AC = 2 √(10) cm, then the length of AQ is:

In Δ ABC, ∠ C = 90º and Q is the midpoint of BC. If…

In $\Delta$ ABC, $\angle$ C = 90º and Q is the midpoint of BC. If AB = 10 cm and AC = 2 $\sqrt{10}$ cm, then the length of AQ is:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. $\sqrt{55}$ cm

In the triangle ABC by using the Pythagoras theorem,

⇒ BC² = (10)² - (2√10)²

⇒ BC² = 100 - 40

⇒ BC = 2√15 cm

As Q is the midpoint of BC

⇒ QC = √15 cm

Again by applying Pythagoras theorem,

⇒ AQ² = (2√10)² + (√15)²

⇒ 40 + 15

⇒ AQ = √55 cm