Question

The perimeter of a triangle is equal to 12 inches. The length of the longest side is equal to the sum of the other two sides minus 2. If you multiply the shortest side by 3 and add one, it will equal twice the longest side. Find the side lengths.

Answer 1

@Elysse2012 I have done some work on this problem but I need you to check it. If you have not already solved it, let me know.

Answer 2

yeah?

Answer 3

Let L represent the longest side of the triangle.
Let M represent the second longest side of the triangle.
Let S represent the smallest side of the triangle.

Now, to write the equations.

Answer 4

The perimeter of a triangle is equal to 12 inches.
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L + M + S = 12

Answer 5

length of the longest side is equal to the sum of the other two sides minus 2.
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L = M + S - 2

Answer 6

multiply the shortest side by 3 and add one, it equals twice the longest side
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3S + 1 = 2L

Answer 7

Agree with those three equations as accurate expressions of the relationships of the sides of this triangle? @Elysse2012

Answer 8

Waiting for a reply before I proceed.

Answer 9

@Elysse2012 Agree or disagree with the three equations?

Answer 10

agree

Answer 11

1) L + M + S = 12

2) L = M + S - 2 --> L - M - S = -2

3) 3S + 1 = 2L

Answer 12

Add the terms of equations (1) and (2)

1) L + M + S = 12
2) L - M - S = -2
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2L + 0 + 0 = 10
2L = 10

L = ? @Elysse2012

Answer 13

5

Answer 14

Take the third equation:

3) 3S + 1 = 2L
3S + 1 = 2*5 where L =5 from above work.

Solve the equation for S (no decimals at this point, please) @Elysse2012

Answer 15

3S+1=32
3S=31
S= 10 1/3

Answer 16

OH OOPP..

Answer 17

nevermind

Answer 18

wait.... is that right?

Answer 19

I am not following how this:

3S + 1 = 2L
3S + 1 = 2*5
3S + 1 = 10

became this:

3S+1=32
3S=31

I may have messed you up talking about decimals. I had a typo of 17 as the perimeter which is not right and sent me to fraction-ville.

Answer 20

>wait.... is that right? NO

Answer 21

Solve this for S: 3S + 1 = 10
We're almost finished.

Answer 22

@Elysse2012 Question?

Answer 23

sorry I didn't look carefully at the 2*5.. thought it was a 2^5

Answer 24

3S = 9
S=3

Answer 25

and so M is 4

Answer 26

Yes. That's correct.

Answer 27

ok :) thank you!

Answer 28

Glad to help.