All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Packing 'em In (Posted on 2004-03-02) Difficulty: 3 of 5

ABC is an acute-angled triangle with area 1. A rectangle F(PQRS) has its vertices on the sides of the triangle, with P and Q on BC, R on AC, and S on AB. Another rectangle, G(WXYZ), has its vertices on the sides of triangle ASR, with W and X on RS, Y on AS, and Z on AR.

What is the maximum total area of F and G?

See The Solution Submitted by DJ    
Rating: 4.2000 (10 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Layman's Maths | Comment 7 of 13 |

For this I needed to add some figures into the picture, I called the line BC = 10cm, dropping a perpendicular line from A to an intersection of BC, say A-A', i called this length 10cm also,

this gives us an area for the triangle of 50cm², (base x 1/2 height)

now i need to insert 2 squares into the triangle, i used the equation ½height x ½width (5cm x 5cm) for the first (F) and ¼height x ¼width (2.5cm x 2.5cm) for the second (G)

from this i can now work out area of F+G to be 25cm²+6.25cm²=31.25cm²

this is 62.5% of the original triangles area

 


  Posted by Juggler on 2004-03-03 02:07:02
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information