Q4 of 58 Page 108

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Consider a right angle ΔABC


Let the base of the Δ be x


⇒ Altitude = x - 7


In the right-angled triangle


According to the Pythagoras theorem


(Hypotenuse)2 = (base)2 + (altitude)2


⇒ 132 = x2 + (x - 7)2


⇒ 169 – x2 – x2 - 49 + 14x = 0


⇒ 2x2 - 14x – 120 = 0


⇒ x2 – 7x - 60 = 0


⇒ x2 – 12x + 5x - 60 = 0


⇒ x( x - 12) + 5( x – 12) = 0


⇒ (x + 5) (x - 12) = 0


⇒ x = - 5 or 12


But base cannot be negative, so x = 12 cm


⇒ altitude = 12 - 7 = 5 cm


Hence 5 cm and 12 cm are the two sides of the given triangle.


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