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Ex 4.2, 5 The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides. Let ABC be right angled triangle, with altitude = AB, Base = BC & Hypotenuse = AC Given Hypotenuse = AC = 13 cm And, Altitude is 7 cm less than base Let Base = BC = x cm ∴ Altitude = AB = Base – 7 = x – 7 Since ABC is a right angled triangle Using Pythagoras theorem Hypotenuse2 = Height2 + Base2 (AC) 2 = AB2 + BC2 (13)2 = (x – 7)2 + x2 169 = x2 + 49 – 14x + x2 169 = 2x2 – 14x + 49 0 = 2x2 – 14x + 49 – 169 0 = 2x2 – 14x – 120 2x2 – 14x – 120 = 0 2 (x2 – 7x – 60) = 0 x2 – 7x – 60 = 0 We factorize by splitting the middle term method x2 + 5x – 12x – 60 = 0 x (x + 5) – 12 (x + 5) = 0 (x – 12) (x + 5) = 0 So, x = 12 , x = –5 are the roots of the equation Since x is length, it cannot be negative Thus, x = 12 Therefore, Base = x = 12 cm Altitude = x – 7 = 12 – 7 = 5 cm x – 12 = 0 x = 12 x + 5 = 0 x = –5

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.