
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 20th, 2012, 02:21 AM  #1 
Member Joined: Jan 2012 Posts: 52 Thanks: 0  Max. area of an inscribed rectangle
Hello, How do I find the maximum area (the biggest value of the area) of a rectangle in the following case: Be a, b, c the sides of a right triangle such the If x and y are the sides of a rectangle such as x belongs to the side b and y to the side c of triangle and one vertex of the rectangle touches the side a, find the maximum value for x.y in terms b and c. Thanks! 
June 20th, 2012, 04:49 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: Max. area of an inscribed rectangle
Under such a constraint, the largest rectangular shape, in terms of area, is a square, so x = y. Using the formula for the area, A, of a triangle we have A = bc/2. Sketching a diagram we observe that the area of the triangle can be written as So the greatest area is . 
June 20th, 2012, 05:04 AM  #3  
Member Joined: Jun 2012 From: UK Posts: 39 Thanks: 0  Re: Max. area of an inscribed rectangle Quote:
Largest area, bc/4, occurs when x=b/2 and y=c/2.  
June 20th, 2012, 05:56 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: Max. area of an inscribed rectangle
You're right  again. I had bc/4 as a solution, but discarded it after an erroneous calculation. 

Tags 
area, inscribed, max, rectangle 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Area of a rectangle  guru123  Algebra  2  May 19th, 2012 10:36 PM 
Rectangle Area Approximation  jaredbeach  Calculus  4  January 10th, 2012 06:47 PM 
problem in area of rectangle  simranjit  Algebra  5  November 28th, 2010 10:12 PM 
Comparing perimeter and area of the inscribed polygons  magician  Algebra  1  October 12th, 2009 03:33 AM 
Rectangle ARea  djodyssey1127  Algebra  3  January 22nd, 2008 10:18 PM 