Q1 of 45 Page 43

Some questions and their alternative answers are given. Select the correct alternative.

Altitude on the hypotenuse of a right angled triangle divides it in two parts of lengths 4 cm and 9 cm. Find the length of the altitude.



Let ABC be a right-angled triangle, at B, and BP be the altitude on hypotenuse that divides it in two parts such that,


AP = 4 cm


PC = 9 cm


As, ABC, ABP and CBP are right-angled triangles, therefore they all satisfy Pythagoras theorem i.e.


(Hypotenuse)2 = (base)2 + (Perpendicular)2


∴ In ΔABC


AB2 + BC2 = AC2


⇒ AB2 + BC2 = (AP + CP)2


⇒ AB2 + BC2 = (4 + 9)2 = 132


⇒ AB2 + BC2 = 169 [1]


∴ In ΔABP


AP2 + BP2 = AB2


AP2 + 42 = AB2 [2]


∴ In ΔCBP


CP2 + BP2 = BC2


⇒ 92 + BP2 = BC2 [3]


Adding [2] and [3], we get


AP2 + 42 + 92 + BP2 = AB2 + BC2


⇒ 2AP2 + 16 + 81 = 169 [From 1]


⇒ 2AP2 = 72


⇒ AP2 = 36


⇒ AP = 6 cm


Hence, length of Altitude is 6 cm.

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