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 result:

S =  24 cm2

Solution:

r=5 cm c=2⋅ r=2⋅ 5=10 cm c2=a2+b2 a=c−2d b=c−d c2=(c−2d)2+(c−d)2  102=(10−2d)2+(10−d)2  102=(10−2⋅ 2)2+(10−2)2  d<c d=d2=2 b=c−d=10−2=8 cm a=c−2⋅ d=10−2⋅ 2=6 cm S=a⋅ b/2=6⋅ 8/2=24 cm2

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