SOLUTION: What is the maximum area of a triangle having 15 cm as the sum of its base and height ?
Algebra.Com
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) (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.
RELATED QUESTIONS
What is the maximum area of a triangle having 15cm as the sum of its base and height ?... (answered by scott8148)
Determine the maximum area of a triangle, in square centimeters, if the sum of its base... (answered by checkley77)
The sum of the base and height of a triangle is 25 cm. What is the maximum area of the... (answered by solver91311)
The sum of the base and height of a triangle is 25 cm. What is the maximum area of the... (answered by ankor@dixie-net.com)
The sum of the base and the height of a triangle is 18 cm. Find the dimensions for which... (answered by Alan3354,ikleyn,josgarithmetic)
The sum of the base and the height of a triangle is 10 cm. Find the dimensions for which... (answered by ladyVenny)
Suppose the base and height of a triangle sum to 15, and the area of the triangle is 20... (answered by lwsshak3)
if the sum of the base and the height of a triangle is 16 cm, what are the dimensions for (answered by Fombitz)
3) Find the height of a triangle if it's area is 22 cm² and its base is 15 cm ?
(answered by Fombitz)