perplexus.info :: Just Math : Side constraint for maximizing area

Side constraint for maximizing area (Posted on 2023-09-04)

Let ABC be a triangle with side lengths a, b, c and a=2, b+2c=4. Find the value of c which maximizes the area of the triangle.

No Solution Yet Submitted by Danish Ahmed Khan

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computer approximation

| Comment 1 of 7

clc

a=2; prev=0;

for b= 1.82970846:.000000002: 1.82970849

c=(4-b)/2;

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

A=sqrt(s*(s-a)*(s-b)*(s-c));

if A==real(A)

disp([b c A A-prev])

end

prev=A;

end

is the final stage of the program after narrowing down the range, and finds the maximal area as:

      b              c                Area
      
1.829708486     1.085145757     0.98402327954184

Posted by Charlie on 2023-09-04 12:27:26

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