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If the sum of the lengths of the hypotenuse and another side of a right angled triangle is given then the area of the triangle is maximum when the angle between those sides is

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The Brainliest Answer!

base=x

so, h+x=a

a=constant

laet area be A then,

A=1/2(x*(√h*h-x*x)

squaring both side

A*A={ (a*a)(x*x)-2a(x*x*x) }/4

then differentiate

2dA/dX=1/4{2a*a*x-6*a*x*x}

for maxima

dA/dX=0

then 1/8A(2*a*a*x-6*a*x*x)=0

x=a/3

then cosΘ=x/a-x

cosΘ=(a/3)/(a-a/3)

cosΘ=1/2=cosπ/3

Θ=π/3