My Math Forum  

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

Geometry Geometry Math Forum


Reply
 
LinkBack Thread Tools Display Modes
April 2nd, 2013, 07:55 PM   #1
Newbie
 
Joined: Apr 2013

Posts: 6
Thanks: 0

Geometry(Triangle)/Algebra(Probability) Problem

A triangle will be called almost equilateral if the sum of the differences between all pairs of sides is 6 or less. Thus, a 3-4-5 triangle is almost equilateral, since 1 + 2 + 1 = 4. However, a 4-6-8 triangle is not, since 2 + 4 + 2 = 8.

How many almost equilateral triangles are there with sides whose lengths are integers 100 or less, and such that no side length ends in the digits 4 or 6? (Note: a 3-4-5 triangle is considered the same as a a 3-5-4 triangle; the order of the sides does not matter.)

Any and all help is much appreciated. Thank you!
ItisBowtime is offline  
 
April 2nd, 2013, 07:57 PM   #2
Newbie
 
Joined: Apr 2013

Posts: 6
Thanks: 0

Re: Geometry(Triangle)/Algebra(Probability) Problem

I also have a variant on the same problem that I also must solve:
How many almost equilateral triangles are there with sides whose lengths are integers 100 or less, and such that no side length ends in the digit 6?

Once again, any and all help is much appreciated. Thank you and have a good day!
ItisBowtime is offline  
April 2nd, 2013, 08:34 PM   #3
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 10,103
Thanks: 684

Re: Geometry(Triangle)/Algebra(Probability) Problem

Quote:
Originally Posted by ItisBowtime
A triangle will be called almost equilateral if the sum of the differences between all pairs of sides is 6 or less. Thus, a 3-4-5 triangle is almost equilateral, since 1 + 2 + 1 = 4. However, a 4-6-8 triangle is not, since 2 + 4 + 2 = 8.

How many almost equilateral triangles are there with sides whose lengths are integers 100 or less, and such that no side length ends in the digits 4 or 6? (Note: a 3-4-5 triangle is considered the same as a a 3-5-4 triangle; the order of the sides does not matter.)
I get 870.
1st 4: 1-2-2, 1-3-3, 1-4-4, 2-2-3
last 4: 98-99-100, 98-100-100, 99-99-100, 99-100-100

Call the sides a-b-c
a=1: 3
a=2: 6
a=3: 8

a=4 to 97: 9

a=98: 5
a=99: 2
a=100: 0

3 + 6 + 8 + 94*9 + 5 + 2 + 0 = 870

b-a + c-a + c-b = 2c - 2a
2c - 2a = 6
c - a = 3
If c - a <= 3 then ok
Denis is offline  
Reply

  My Math Forum > High School Math Forum > Geometry

Tags
problem



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
A difficult problem in geometry - A Triangle and Two Squares metavdr Geometry 7 February 8th, 2014 07:59 AM
Geometry - Triangle with median problem sachinrajsharma Geometry 1 March 27th, 2013 10:49 AM
Urgent help with this algebra cum geometry problem pksinghal Geometry 11 July 3rd, 2010 03:23 PM
Geometry + Probability Problem Charmed Geometry 6 March 4th, 2010 05:04 PM
Geometry - Isosceles triangle problem pksinghal Geometry 3 January 18th, 2010 06:03 AM





Copyright © 2017 My Math Forum. All rights reserved.