Ask Experts Questions for FREE Help !
Ask
    ray13971's Avatar
    ray13971 Posts: 3, Reputation: 1
    New Member
    		  
    #1

    Nov 28, 2010, 12:10 PM
    length of a triangle
    The lengths of the sides of a triangle are consecutive even integers.Find the length of the longest side if it is 14 units shorter than the perimeter
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
    		  
    #2

    Nov 28, 2010, 01:58 PM

    Since the sides are consecutive even integers, it has perimeter
    P=x+(x+2)+(x+4)

    If you are familiar with Pythagorean triangles, this alone gives away the solution.

    By Pythagoras:



    Solve for x. You will notice the length of the hypoteneuse is 14 shorter than the perimeter.
    It works out that way.
    harum's Avatar
    harum Posts: 339, Reputation: 27
    Full Member
    		  
    #3

    Nov 28, 2010, 09:53 PM
    Quote Originally Posted by galactus View Post
    If you are familiar with Pythagorean triangles, this alone gives away the solution.
    Looks like we have no reason to assume that the solution is a right angle triangle and ignore that the perimeter is longer than the longest side by a certain number.
    Wouldn't it be just this (here a is the shortest side)?

    a + (a+2) + (a+4) = (a+4) + 14 => a = 6 and so on.
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
    		  
    #4

    Nov 29, 2010, 02:12 AM

    I was thinking this as well... the triangle is not necessarily a right angled triangle.

    Or, if we want to go faster, we do:

    Let the longest side be x.

    P - 14 = x
    P = (x-4) + (x-2) + x

    [(x-4) + (x-2) + x] - 14 = x
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
    		  
    #5

    Nov 29, 2010, 02:24 PM

    Yes, my bad. False assumption.

    Force of habit. I am so used to these problems involving right triangles.

    Coincidentally, I had just gone over a problem that stated "one side of a right triangle is 7 units more than the short side, and the hypoteneuse is 8 more than the short side. What are the side lengths?".
Not your question? Ask your question View similar questions
 

Question Tools Search this Question
Search this Question:

Advanced Search

Add your answer here.


Check out some similar questions!

The perimeter of the pool is 97m, the width is more than 1/2 the length,length=? Widt [ 1 Answers ]

The perimeter of the pool is 97m, the width is 2m more than 1/2 the length, what is the length and width of the pool?

Isos Triangle with sides 10,10, and 8. Find length of altitude to a long side. [ 2 Answers ]

So there's an altitude going from the vertex adjacent to the side 8cm long to a side measuring 90 degrees. The altitude creates 2 right triangles within and so they share one side. Here's a image I drew up in paint to help show the problem. http://img521.imageshack.us/img521/2083/isos.png ...

What is A of a right triangle when a=2 and b=12 [ 1 Answers ]

What is A of a right triangle when a-2 and b=12?

Converting Slope arc Length to Flat Arc Length [ 1 Answers ]

Hi, Given parameters are:- Slope arc length Angle on Slope

View more questions Search