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In a triangle, one side is twice as long as the shortest side and another is two inches less than four times the shortest side. If the perimeter of the triangle is 33 inches, what are the side lengths?

 Sep 12, 2020
 #1
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In a triangle, one side is twice as long as the shortest side and another is two inches less than four times the shortest side. If the perimeter of the triangle is 33 inches, what are the side lengths?    

 

Let's call the three sides of this triangle A, B, and C  

 

Let's let C be the shortest side.  No particular reason, I just picked one.  

 

Now "one side is twice as long as the shortest side" so let's let this side be A     thus  A  =  2C                   (1)

 

And "another is two inches less than four times the shortest side"                       thus  B  =  4C – 2             (2)

 

And finally "the perimeter of the triangle is 33 inches"                                          thus  A + B + C  =  33  

 

Can you solve it now, by the substitution method?  I'll get you started. 

 

Start with the A+B+C and substitute for A and B                                                     A  +      B      + C  =  33

 

Substitute terms from (1) and (2)                                                                           2C + (4C – 2) + C  =  33  

 

Add up all the C's                                                                                                   7C          – 2           =  33    

 

Add 2 to both sides of the equation                                                                        7C                          =  35  

 

Divide both sides by 7                                                                                                                       C  =  5    

 

Now go back up and substitute 5 for C in the equalities for A and B.                        A  =  10   and   B  =  18  

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 Sep 13, 2020
 #4
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Who gave the thumbs down for this?  The solution is accurate and, if I do say so myself, clear and easy for young students to understand how to achieve it.  So why the thumbs down?  It isn't my fault that the problem describes a triangle that can't exist. 

 

I'm going back to answer questions in the Knowledge Base on eBay.  No hateful trolls giving me unhelpfuls.  They appreciate help over there, where, incidentally, I was accepted into the mentor group and have 18,378 Helpfuls as of this writing  It might be immodest for me to toot my own horn, but if I don't, who else will?  And, as the great Muhammad Ali said, It ain't bragging if you can do it. 

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Guest Sep 13, 2020
 #2
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+1

Call the sides x,y,and z.

 

Writing equations, just random, 2z=x, 4z-2=y, and x+y+z=33.

 

z=shortest side.

 

So x=10, y=18, and z=5.

 

BUT WAIT!

 

By the triangle inequality, x+z>y

and it isn't

so that question is WRONG.

 Sep 13, 2020
 #3
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+1

 

Hi Pangolin.  I'm the guest from answer #1.  I didn't even notice the impossibility.  Good catch. 

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Guest Sep 13, 2020

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