My Math Forum  

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

Geometry Geometry Math Forum

LinkBack Thread Tools Display Modes
December 15th, 2013, 12:04 AM   #1
Joined: Dec 2013

Posts: 86
Thanks: 1


Q: In a right triangle ABC,what is the maximum possible area of a square that can be inscribed when one of its vertices coincide with the vertex of the right angle of the triangle ?





Ansd). Now can this question be solved algebraically without using trigonometric ratios? Request a non-trigonometric solution.
Thanks in advance!
Attached Images
File Type: jpg untitled.JPG (15.0 KB, 80 views)
Aman Verma is offline  
December 15th, 2013, 12:28 AM   #2
Senior Member
MarkFL's Avatar
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,209
Thanks: 517

Math Focus: Calculus/ODEs
Re: Geometry-Triangle

Let the triangle above the square, which is similar to the larger triangle in which the square is inscribed have base and height .

The area of the square is then:

By similarity, we have:

We also have:


And so:

MarkFL is offline  
December 15th, 2013, 01:40 AM   #3
Math Team
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 13,795
Thanks: 970

Re: Geometry-Triangle

BC = a, AC = b, square sides = x; then AD = b - x and BF = a-x :


F      x        E

x               x

C      x        D        b-x          A
Since triangle BEF is similar to triangle EAD:
(a - x) / x = x / (b - x)
x^2 = (a - x)(b - x)
x^2 = ab - ax - bx + x^2
ax + bx = ab
x = ab / (a + b) ........area = x^2
Denis is offline  

  My Math Forum > High School Math Forum > Geometry


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
Geometry: Incircle of a Triangle fishsticks1907 Geometry 2 June 5th, 2012 11:05 AM
Geometry, triangle question. fishsticks1907 Geometry 5 May 23rd, 2012 01:08 PM
triangle geometry biosavart Geometry 6 December 8th, 2010 08:37 PM
Geometry Triangle Proof meph1st0pheles Geometry 1 January 31st, 2010 08:51 PM
Geometry - triangle macciej Geometry 3 October 26th, 2009 09:31 PM

Copyright © 2019 My Math Forum. All rights reserved.