3±2√3 much longer is the longer leg when in a right triangle, the hypotenuse is 2 cm longer than the longer leg, while one of the legs is 1 cm shorter than the other.
Given that,
In a right triangle, the hypotenuse is 2 cm longer than the longer leg, while one of the legs is 1 cm shorter than the other.
We have to find how much longer is the longer leg.
We know that,
Let the one side of the triangle be x
The other side we get x-1 and x+2
From Pythagoras theorem,
x²+(x-1)²=(x+2)²
x²+x²-2x+1=x²+4x+4
2x²-2x+1-x²-4x-4=0
x²-6x-3=0
To find the value of x we have a formula that is
x=-b±√(b²-4ac)/2a
Here, a=1, b=-6 c=-3
x=6±√(-6²-4(1)(-3))/2(1)
x=6±√36+12/2
x=6±√48/2
x=6±4√3/2
x=3±2√3
Therefore, 3±2√3 much longer is the longer leg when in a right triangle, the hypotenuse is 2 cm longer than the longer leg, while one of the legs is 1 cm shorter than the other.
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