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The lengths of the sides of a triangle. . . . .

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by Vincen » Wed Sep 27, 2017 5:58 pm
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

The OA is E.

I got confused because of the ratio among the sides. Can any expert clarify the meaning for me? Thanks.
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by [email protected] » Wed Sep 27, 2017 8:04 pm
Hi Vincen,

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.

Final Answer: E

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by Vincen » Fri Sep 29, 2017 7:23 pm
Thanks Rich. Your explanations are really helpful to me.
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by Jeff@TargetTestPrep » Tue Oct 03, 2017 3:15 pm
Vincen 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.

Answer: E

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by EconomistGMATTutor » Sat Oct 07, 2017 2:10 pm
Vincen 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

The OA is E.

I got confused because of the ratio among the sides. Can any expert clarify the meaning for me? Thanks.
Hi Vincen,
Let's take a look at your question.

The question states that the lengths of the sides of a triangle are in the ratio of 3 to 5 to 6.
Let the lengths of the sides of the triangle be 3x, 5x and 6x and the perimeter is 70.
Then,
Sum of the sides of the triangle = Perimeter
3x + 5x + 6x = 70
14x = 70
x = 70/14
x = 5

The longest side of the triangle = 6x = 6 x 5 = 30
Therefore, Option E is correct.

I am available if you'd like any followup.
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