SOLUTION: Hi I would like a calculus answer to this problem (Using a derivative) What is the maximum area of a right angled triangle with perimeter 72? thank you!

Question 894103: Hi I would like a calculus answer to this problem (Using a derivative)
What is the maximum area of a right angled triangle with perimeter 72?
thank you!
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Form a right triangle, sides A and B, hypotenuse C.
Perimeter:

Pythagorean theorem:

Let's get rid of

.
.

Area (Use Y instead of A):

Maximize the area.
Make Y a function of only 1 variable.
Substitute,

Take the derivative using the quotient rule,

Now set it equal to zero.

Since cannot be greater than 72,

Then,

It's an isosceles right triangle.
So then,

RELATED QUESTIONS
Hi! Can you please help me solve this problem? I need to find the area of a right... (answered by richwmiller)

Finding the derivative using the defintion? hi i would like to find out how to solve... (answered by jim_thompson5910)

How to find the Maximum Area of the Rectangle inscribed in a Right Triangle of sides a, b (answered by solver91311)

Hi. I have tried this problem over and over, and came up with this solution: (2√2A (answered by josgarithmetic)

Hi! Can you please help me to answer this question? The other day I was helping a... (answered by Fombitz)

hi, would you please help me solve this multiple choice question?: one leg of a right... (answered by amarjeeth123)

Hi! Can you please help me with this problem? It's pretty simple, from what I can tell,... (answered by rothauserc)

respected sir, 1] Area of a right-angled triangle is doubled while the base is reduced (answered by Alan3354)

This is a question from the chapter 'Sets' which is related to Geometry: Triangles.... (answered by rfer)