SOLUTION: What is the maximum area of a triangle having 15 cm as the sum of its base and height ?

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Question 957123: What is the maximum area of a triangle having 15 cm as the sum of its base and height ?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
This is the equivalent of asking the maximum product for two numbers whose sum is 15.
Let x=base and y=height
x+y=15
y=15-x
f(x)=xy=x(15-x)
f(x)=15x-x^2 Differentiate this function.
f'(x)=15-2x Maximum value of f(x) occurs when f'(x)=0
0=15-2x Add 2x to each side.
2x=15
x=7.5 ANSWER 1: The base is 7.5 cm
y=15-x=15-7.5=7.5 ANSWER 2: The height is is 7.5 cm
The length of base and height for maximum area would both be 7.5 cm.