the hypothnue of right triangle is 2 more than twice of one ofthe other side while the 3rd side is 13 more than half of the hypoth

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1. Step-by-step explanation:

   Given :–

   The hypothnue of right triangle is 2 more than twice of one ofthe other side while the 3rd side is 13 more than half of the hypotenuse.

   To find :–

   Find the length of all the sides ?

   Solution :–

   Let the one side of the right angled triangle be X units

   Then the hypotenuse of the right angled triangle

   = 2 more than twice of the one side of the triangle

   = (2X+2) units

   The length of the third side

   = 13 more than half of the hypotenuse

   = (2X+2)/2 + 13

   => 2(X+1)/2 + 13

   => X+1+13

   => (X+14) units

   The lengths are X units , (2X+2) units , (X+14) units

   We know that

   By Pythagoras theorem

   Hypotenuse^2 = 1st Side^2 + 2nd Side^2

   => (2X+2)^2 = X^2+(X+14)^2

   => (2X)^2+2(2X)(2)+2^2 = X^2+X^2+2(X)(14)+14^2

   Since (a+b)^2 = a^2+2ab+b^2

   => 4X^2+8X+4 = 2X^2+28X+196

   => 4X^2+8X+4-2X^2-28X-196 = 0

   => 2X^2-20X-192 = 0

   => 2(X^2-10X-96) = 0

   => X^2-10X-96 = 0/2

   =>X^2-10X-96 = 0

   => X^2+6X-16X-96 = 0

   => X(X+6) -16(X+6) = 0

   => (X+6)(X-16) = 0

   =>X+6 = 0 or X-16 = 0

   => X = -6 or X = 16

   X cannot be negative

   X = 16 units

   One side = 16 units

   Hypotenuse = 2X+2

   => 2(16)+2

   => 32+2

   => 34 units

   Third side = (34/2)+14

   => 17+13

   => 30 units

   The measurements are 16 units ,34 units ,

   30 units

   Answer:–

   The measurements of all the sides of the right angled triangle are 16 units , 34 units and

   30 units

   Used formulae:–

   Pythagoras Theorem:–

   In a right angled triangle,the square of the hypotenuse is equal to the sum of the squares of the other sides.

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