Mathematics
The altitude of a right triangle is 17 cm less than its base. If the hypotenuse is 25 cm, then the perimeter of the triangle is :
48 cm
56 cm
54 cm
64 cm
Quadratic Equations
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Answer
Let the base and height of right triangle be x cm and (x - 17) cm respectively.
By pythagoras theorem,
⇒ Base2 + Height2 = Hypotenuse2
⇒ x2 + (x - 17) 2 = (25)2
⇒ x2 + x2 + (17)2 - 2 × x × 17 = 625
⇒ x2 + x2 + 289 - 34x = 625
⇒ 2x2 - 34x + 289 - 625 = 0
⇒ 2x2 - 34x - 336 = 0
⇒ 2(x2 - 17x - 168) = 0
⇒ x2 - 17x - 168 = 0
⇒ x2 - 24x + 7x - 168 = 0
⇒ x(x - 24) + 7(x - 24) = 0
⇒ (x + 7)(x - 24) = 0
⇒ (x + 7) = 0 or (x - 24) = 0 [Using zero -product rule]
⇒ x = -7 or x = 24.
Since, the length of triangle cannot be negative, x ≠ -7.
x - 17 = 24 - 17 = 7.
The perimeter of right triangle is = 7 + 24 + 25 = 56 cm.
Hence, option 2 is the correct option.
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