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

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

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
2 years ago
Dear Student

Given,
the altitude of right triangle = (x - 7) cm
From Pythagoras theorem,
we know, Base^2 + Altitude^2 = Hypotenuse^2
x^2 + (x - 7)^2 = 13^2
⇒ x^2 + x^2 + 49 - 14x = 169
⇒ 2x^2 - 14x - 120 = 0
⇒ x^2 - 7x - 60 = 0
⇒ x^2 - 12x + 5x - 60 = 0
⇒ x(x - 12) + 5(x - 12) = 0
⇒ (x - 12)(x + 5) = 0
Thus, either x - 12 = 0 or x + 5 = 0,
⇒ x = 12 or x = - 5
Since sides cannot be negative, x can only be 12.
the base of the given triangle is 12 cm and the altitude of this triangle will be (12 - 7) cm = 5 cm.

Thanks

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