SOLUTION: The sum of the base and the height of a triangle is 48cm. Find the dimensions for which the area is maximum. SHOW ALGEBRAICALLY. Draw and label the picture.
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Question 583299: The sum of the base and the height of a triangle is 48cm. Find the dimensions for which the area is maximum. SHOW ALGEBRAICALLY. Draw and label the picture.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You don't need to yell. We can read.
Let 
be the constant sum of the base and height of a triangle. Hence:
Solving for 
Substitute for in the formula for the area of a triangle to create an Area formula as a function of 
.
\ =\ \frac{b(C\ -\ b)}{2})
\ =\ \frac{Cb\ -\ b^2}{2})
Take the first derivative:
Set the first derivative equal to zero and solve
is a local extreme.
Take the second derivative:
which is negative for all values of the variable, hence the extreme is a maximum.
Substitute back into the original relationship between and :
Hence the area is maximum when the base is equal to the height.
John
My calculator said it, I believe it, that settles it
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