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Math Expert V
Joined: 02 Sep 2009
Posts: 59712
The lengths of the sides of a triangle are in the ratio of 3 to 5 to 6  [#permalink]

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Difficulty:   5% (low)

Question Stats: 89% (00:41) correct 11% (01:11) wrong based on 77 sessions

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The lengths of the sides of a triangle are in the ratio of 3 to 5 to 6. If the perimeter of the triangle is 70, what is the length of the longest side?

(A) 5
(B) 6
(C) 15
(D) 25
(E) 30

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Joined: 02 Sep 2016
Posts: 14
GMAT 1: 660 Q50 V29 Re: The lengths of the sides of a triangle are in the ratio of 3 to 5 to 6  [#permalink]

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Let the sides of the triangle are
3k,5k and 6k
Given perimeter(3k+5k+6k) =70
Solving for k, k =5.
So longest side of the triangle is 6k =6*5=30

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Re: The lengths of the sides of a triangle are in the ratio of 3 to 5 to 6  [#permalink]

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the length of the longest side is = 6/14 * 70 = 30

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The lengths of the sides of a triangle are in the ratio of 3 to 5 to 6  [#permalink]

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1
Hi All,

We're told that the ratio of the lengths of the sides of a triangle are 3 to 5 to 6 and that the perimeter of the triangle is 70. We're asked for the length of the longest side.

When it comes to ratios questions on the GMAT, you will almost always be dealing with integers (and while there are some exceptions, they're relatively rare). Thus, the first side of this triangle will likely be an integer multiple of 3, the second side an equivalent multiple of 5 and the third side an equivalent multiple of 6. By extension, the SUM of the sides will be a multiple of 14.

For example:
3, 5 and 6 -- Perimeter = 14
6, 10 and 12 -- Perimeter = 28
9, 15 and 18 -- Perimeter = 42
Etc.

Since we know the perimeter = 70 and 70 = (14)(5), we know that each side is 5 times the number in the ratio. In this case, the three sides would be 15, 25 and 30.

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Re: The lengths of the sides of a triangle are in the ratio of 3 to 5 to 6  [#permalink]

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Bunuel wrote:
The lengths of the sides of a triangle are in the ratio of 3 to 5 to 6. If the perimeter of the triangle is 70, what is the length of the longest side?

(A) 5
(B) 6
(C) 15
(D) 25
(E) 30

We can let the sides of the triangle = 3x, 5x, and 6x; thus:

3x + 5x + 6x = 70

14x = 70

x = 5

Thus, the longest side is 6(5) = 30.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: The lengths of the sides of a triangle are in the ratio of 3 to 5 to 6   [#permalink] 05 Jan 2018, 08:08
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