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# A triangle has sides with lengths x – 2, 2x – 3 and x + 1. If the peri

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Joined: 02 Sep 2009
Posts: 54437
A triangle has sides with lengths x – 2, 2x – 3 and x + 1. If the peri  [#permalink]

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29 Aug 2017, 02:26
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87% (00:57) correct 13% (00:41) wrong based on 34 sessions

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A triangle has sides with lengths x – 2, 2x – 3 and x + 1. If the perimeter of the triangle is 20, what is the length of the longest side?

(A) 9
(B) 8
(C) 7
(D) 6
(E) 5

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Re: A triangle has sides with lengths x – 2, 2x – 3 and x + 1. If the peri  [#permalink]

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29 Aug 2017, 02:31
Bunuel wrote:
A triangle has sides with lengths x – 2, 2x – 3 and x + 1. If the perimeter of the triangle is 20, what is the length of the longest side?

(A) 9
(B) 8
(C) 7
(D) 6
(E) 5

x-2+2x-3+x+1 = 20
x=6
sides will be 4, 9, 7

A
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Re: A triangle has sides with lengths x – 2, 2x – 3 and x + 1. If the peri  [#permalink]

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29 Aug 2017, 02:47
Bunuel wrote:
A triangle has sides with lengths x – 2, 2x – 3 and x + 1. If the perimeter of the triangle is 20, what is the length of the longest side?

(A) 9
(B) 8
(C) 7
(D) 6
(E) 5

Perimeter $$= (x -2) + (2x-3)+ (x+1) = 20$$

$$x - 2 + 2x - 3 + x + 1 = 20$$

$$4x - 4 = 20$$

$$4x = 20+4 = 24$$

$$x = \frac{24}{4} = 6$$

Lets put value of $$x$$ in the above sides to check which side is longest side.

$$x – 2 = 6 - 2 = 4$$

$$2x – 3 = (2*6) - 3 = 12-3 = 9$$

$$x + 1 = 6 + 1 = 7$$

Therefore Sides are $$4,7$$ and $$9$$.

Longest side $$= 9$$

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Posts: 2825
Re: A triangle has sides with lengths x – 2, 2x – 3 and x + 1. If the peri  [#permalink]

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01 Sep 2017, 12:06
Bunuel wrote:
A triangle has sides with lengths x – 2, 2x – 3 and x + 1. If the perimeter of the triangle is 20, what is the length of the longest side?

(A) 9
(B) 8
(C) 7
(D) 6
(E) 5

We can create the following equation:

x - 2 + 2x - 3 + x + 1 = 20

4x - 4 = 20

4x = 24

x = 6

The longest side is 2(6) - 3 = 9.

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Re: A triangle has sides with lengths x – 2, 2x – 3 and x + 1. If the peri   [#permalink] 01 Sep 2017, 12:06
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