uteta15p2 q101

101In a right triangle, the square of hypotenuse is equal to twice the product of remaining two sides. If the base of this triangle is 12 cm, then the perpendicular of triangle will be

Option : A
Explanation : Given condition is,
h² = 2 (6 × p)
⇒ h² = 2 (12 × p) (Here, p = Perpendicular)
We know that,
h² = b² + p²
⇒ h² = 144 + p²
⇒ 24p = 144 + p²
⇒ p² -24p + 144 = 0
⇒ p² - 12p - 12p + 144 = 0
⇒ p(p - 12)-12(p - 12) = 0
Solving above equation, we get, p = 12
So, the perpendicular of triangle will be 12 cm

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