My Math Forum  

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

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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!
captainglyde is offline  
 
February 19th, 2008, 09:55 AM   #2
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 937

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.
CRGreathouse is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
area, square, 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
Percent of Square's Area symmetry Algebra 15 October 23rd, 2014 11:55 AM
area of square DEFG Albert.Teng Algebra 8 November 20th, 2012 06:27 PM
area of a square Albert.Teng Algebra 4 September 22nd, 2012 10:23 AM
Area of square with convex parts - area of circle gus Algebra 1 April 17th, 2011 05:25 PM
Help me get the square area of my house? Wolv Elementary Math 7 July 18th, 2010 09:11 AM





Copyright © 2017 My Math Forum. All rights reserved.