perplexus.info :: Just Math : Consecutive Side Conundrum

Consecutive Side Conundrum (Posted on 2024-05-15)

The sides of a triangle are three consecutive integers and its inradius is 4. Find the circumradius.

No Solution Yet Submitted by Danish Ahmed Khan

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computer-aided solution

| Comment 1 of 4

for a=1:50

b=a+1; c=b+1;

s=(a+b+c)/2;

inrad=sqrt(s*(s-a)*(s-b)*(s-c))/s;

if inrad==4

R=(a*b*c)/sqrt((a+b+c)*(b+c-a)*(c+a-b)*(a+b-c));

fprintf('%3d %3d %3d %17.15f\n',[a b c R])

end

finds

a b c circumradius
13 14 15 8.125000000000000

i.e., 8 + 1/8

Posted by Charlie on 2024-05-15 12:04:40

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