Q. 44.5( 18 Votes )

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

Answer :

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}

⇒ 13^{2} = x^{2} + (x - 7)^{2}

⇒ 169 – x^{2} – x^{2} - 49 + 14x = 0

⇒ 2x^{2} - 14x – 120 = 0

⇒ x^{2} – 7x - 60 = 0

⇒ x^{2} – 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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