Hypotenuse of right angled triangle is 2 less than 3 times its shortest side.If the remaining side is 2 more than twice the shortest side, find the area of triangle
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Let the shortest side be x.
Hypotenuse = 3x-2
Another side = 2x +2
Now, Applying Pythagorean formula,
(3x-2)^2 = x^2 + (2x+2)^2
9x^2 +4 -12x = x^2 +4x^2+4+8x
4x^2-20x=0
x^2 -5x = 0
x(x-5) = 0
i.e. either x= 0 or x=5.
As x can't be zero so x=5.
So, Shorter side = 5.
Another side will be 12.
Now, Area of triangle = 1/2*b*h = 1/2*5*12 = 30 sq.units
Hypotenuse = 3x-2
Another side = 2x +2
Now, Applying Pythagorean formula,
(3x-2)^2 = x^2 + (2x+2)^2
9x^2 +4 -12x = x^2 +4x^2+4+8x
4x^2-20x=0
x^2 -5x = 0
x(x-5) = 0
i.e. either x= 0 or x=5.
As x can't be zero so x=5.
So, Shorter side = 5.
Another side will be 12.
Now, Area of triangle = 1/2*b*h = 1/2*5*12 = 30 sq.units
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