CBSE Notes, Lectures

CBSE - Mathematics - Quadratic Equations

Quadratic Equations

NCERT Exercise Exercise 4.2

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 the base of the right triangle be x cm.
Its altitude = (x - 7) cm
From Pythagoras theorem, we have
Base2 + Altitude2 = Hypotenuse2
∴ x+ (x - 7)2 = 132
⇒ x2 x+ 49 - 14x = 169
⇒ 2x- 14x - 120 = 0
⇒ x- 7x - 60 = 0
⇒ x- 12+ 5x - 60 = 0
⇒ x(x - 12) + 5(- 12) = 0
⇒ (x - 12)(x + 5) = 0
Either x - 12 = 0 or x + 5 = 0,
⇒ x = 12 or x = - 5
Since sides are positive, x can only be 12.
Therefore, the base of the given triangle is 12 cm and the altitude of this triangle will be (12 - 7) cm = 5 cm.

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