Right-angled triangle

Determine the area of a right triangle whose side lengths form successive members of an arithmetic progression, and the radius of the circle described by the triangle is 5 cm.

Correct answer:

S =  24 cm2

Step-by-step explanation:

r=5 cm c=2 r=2 5=10 cm c2 = a2 + b2 a = c2d b = cd c2 = (c2d)2 + (cd)2  102=(102d)2+(10d)2  5d2+60d100=0 5d260d+100=0 5 ...  prime number 60=2235 100=2252 GCD(5,60,100)=5  d212d+20=0  a=1;b=12;c=20 D=b24ac=1224120=64 D>0  d1,2=2ab±D=212±64 d1,2=212±8 d1,2=6±4 d1=10 d2=2  d<c d=d2=2 b=cd=102=8 cm a=c2 d=102 2=6 cm S=a b/2=6 8/2=24 cm2

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