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.

Algebra ->  Triangles -> 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.       Log On


   

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) About Me  (Show Source):
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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 .





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

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