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

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

GMAT assassins aren't born, they're made,
Rich