If one of the side ribs, which equals x² is hypotenuse, then the other rib length is: b2=(x2)2−(6x)2=x4−36x2.
b=x4−36x2
The perimeter of this triangle is:
P=x2+6x+x4−36x2=80,
x4−36x2=80−x2−6x,
x4−36x2=6,400−80x2−480x−80x2+x4+6x3−480x+6x3+36x2,
12x3−88x2−960x+6,400=0,
3x3−22x2−240x+1,600=0,
(3x3−30x2)+(8x2−240x+1,600)=0,
3x2(x−10)+8(x2−30x+200)=0,
3x2(x−10)+8(x−10)(x−20)=0,
(x−10)(3x2+8x−160)=0,
So, x1 = 10 is one of the roots of this equation.
D = 64 + 1920 = 1984.
x2=6−8+1984=6.09,
x3=6−8−1984=−8.76, which is not possible in our case.
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