Q10 of 18 Page 226

In ΔABC, ∠A = 90°, AB = 5 cm, AC = 12 cm. If AD ⊥ BC, then find AD.

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.


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