Right-angled triangle

Determine the content 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  a=5;b=60;c=100 D=b24ac=60245100=1600 D>0  d1,2=b±D2a=60±160010 d1,2=60±4010 d1,2=6±4 d1=10 d2=2   Factored form of the equation:  5(d10)(d2)=0  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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