My Math Forum  

Go Back   My Math Forum > High School Math Forum > Geometry

Geometry Geometry Math Forum

Thanks Tree1Thanks
  • 1 Post By skipjack
LinkBack Thread Tools Display Modes
June 14th, 2018, 02:06 AM   #1
Joined: Aug 2017
From: India

Posts: 54
Thanks: 2

Maximum area of triangle

Sorry for lot of questions. But please help me to solve this problem
My Attempt:
Area = (1/2) * Base * Height;
Area = (1/2) * p*q;
Maximum is infinite value because p and q can take any value.
Am I correct? Please help. I think I am nowhere near the correct thinking.
Attached Images
File Type: png Q3.PNG (7.9 KB, 8 views)

Last edited by skipjack; June 14th, 2018 at 02:23 AM.
MathsLearner123 is offline  
June 14th, 2018, 02:36 AM   #2
Global Moderator
Joined: Dec 2006

Posts: 21,020
Thanks: 2255

Given the values of p and q, you might as well fix the position of the line segment AB, as doing so won't affect the required area. AB can be called the base of the triangle. The distance of C from AB can be called the height of the triangle. The area of the triangle is maximized when this distance is maximized, because the area is half the product of this distance and p, the length of the base. To maximize the distance of C from AB, BC must be perpendicular to AB, and the maximized distance is then q, the length of BC. The area of triangle ABC is then pq/2.
Thanks from MathsLearner123
skipjack is offline  
June 14th, 2018, 03:12 PM   #3
Senior Member
Joined: Jun 2014
From: USA

Posts: 614
Thanks: 50

From the textbook History of Mathematical Thought (Kline, I believe), it actually hasnt been proven the sum of the angles of a triangle must always add up to 180 degrees. It had something to do with parallel lines not having to be exacty parallel before being provably non-intersecting. The sum of the angles of a triangle can be more than 180 degrees given the assumption. This from a class I took about 15 years ago so sorry not more specific. I assume the above would impact the area.

Hope everyone here is living the good life. Blah.
AplanisTophet is offline  
June 14th, 2018, 04:30 PM   #4
Senior Member
romsek's Avatar
Joined: Sep 2015
From: USA

Posts: 2,576
Thanks: 1423

A far more interesting question is what is the maximum area of a triangle given some properties that limit it's area.

For example what is the maximum area of a triangle with perimeter P.

Or what is the maximum area given a triangle with two sides of length p and q.
romsek is offline  
July 2nd, 2018, 07:05 PM   #5
Senior Member
Joined: Oct 2013
From: New York, USA

Posts: 673
Thanks: 88

Using the semiperimeter formula for the area of a triangle given its sides that I learned here, I think the greatest possible angle with a given perimeter is an equilateral triangle. I don't know if it's possible to prove this by setting a derivative equal to 0 similar to the proof that the given a fixed perimeter the rectangle with the largest area is a square. If the greatest possible area is an equilateral triangle, the maximum area with a perimeter of 3 is all three sides p/3, and the maximum area with sides p and q is p = q = the other side.
EvanJ is offline  

  My Math Forum > High School Math Forum > Geometry

area, maximum, triangle

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
How do I work out the maximum area of a right triangle with a fixed length hypotenuse Gobsheite Calculus 4 June 27th, 2017 10:01 AM
maximum area of triangle panky Trigonometry 4 April 24th, 2017 03:10 PM
Maximum area of a square inscribed in a triangle Volle Calculus 4 July 27th, 2015 03:49 PM
Find the maximum area PlzzHelp Algebra 2 December 5th, 2013 09:45 AM
Maximum and minimum area for n-gon brunojo Algebra 2 November 16th, 2007 10:30 AM

Copyright © 2019 My Math Forum. All rights reserved.