In ΔABC, <span la

In ΔABC, we have ∠A = 90°.

Using Pythagoras theorem, which states the square of hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides,

BC² = AB² + AC²

⇒ BC² = 5² + 12²

⇒ BC² = 25 + 144

⇒ BC² = 169

We know,

As ΔABC is right-angled with ∠A = 90°, we have base = AC and height = AB

∴ Area of ΔABC = 30 cm²

But, it is given that AD ⊥ BC. So area of ΔABC can also be expressed in terms of AD and BC.

Here, we have base = BC and height = AD.

We already found Area of ΔABC = 30 cm²

⇒ 13 × AD = 60

Thus, length of AD is 4.615 cm.