Algebra Pre-Algebra and Basic Algebra Math Forum

 February 19th, 2008, 09:46 AM #1 Newbie   Joined: Oct 2007 Posts: 10 Thanks: 0 area of eq. triangle vs. area of square Without a calculator, using simple mental arithmetic and approximations, I should be able to solve the following problem but I'm having a lot of trouble: One of two ropes equal in length is cut into three segments to form the largest possible triangular area. The other rope is cut into four segments to form the largest possible rectangular area. Which of the following most closely approximates the ratio of the triangle's area to the rectangle's area? 1:2 2:3 3:4 1:1 4:3 (ans: 3:4) Here's how I try to solve this problem but get the wrong answer. If anyone could show me what I'm doing wrong, I'd appreciate it... thank you... if rope is length x, then we have an equilateral triangle of side length (x/3) and a square of side length (x/4). Thus, respective areas should be (x/3)^2sqrt3/4 and (x/4)^2. Simplifying gives x^2sqrt3/9x4 and x^2/16. Multiply both by 4/x^2 should leave sqrt3/9 versus 1/4. How do I look at those numbers and with simple arithmetic say "sqrt3/9:1/4 is approximately 3:4?" Thank you very much! February 19th, 2008, 09:55 AM   #2
Global Moderator

Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: area of eq. triangle vs. area of square

Quote:
 Originally Posted by captainglyde How do I look at those numbers and with simple arithmetic say "sqrt3/9:1/4 is approximately 3:4?"
Well, sqrt(3) is between 3/2 and 2 since 9/4 < 3 < 4. The ratio is thus between 1.5/9:1/4 = 1/6:1/4 = 4:6 = 2:3 and 4/9:1/4 = 16:9. These are both close to 3:4. Tags area, square, triangle ,

,

### eq triagnle

Click on a term to search for related topics.
 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post symmetry Algebra 15 October 23rd, 2014 11:55 AM Albert.Teng Algebra 8 November 20th, 2012 06:27 PM Albert.Teng Algebra 4 September 22nd, 2012 10:23 AM gus Algebra 1 April 17th, 2011 05:25 PM Wolv Elementary Math 7 July 18th, 2010 09:11 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top      