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What is the perimeter?

This topic has 1 expert reply and 2 member replies
phanikpk Senior | Next Rank: 100 Posts Default Avatar
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What is the perimeter?

Post Wed Jun 25, 2014 3:17 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If the area of triangular region RST is 25. What is the perimeter of RST?
    1) THe length of one of the sides is 5(2)^1/2
    2) The triangle is a right isoceles triangle

    I have kept D, anyways B is only sufficient.
    The only way A is sufficient I thought is, since area has to be 25, the side whatever is given cannot be hypotenuse because, if side is 5(2)^1/2, then only we can get 25. If the given triangle is not right triangle the option A cannot hold true.

    If the question has a diagram depicting a right triangle then the answer can be D or not?

    Please help...

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    Post Wed Jun 25, 2014 5:34 pm
    Hi phanikpk,

    I'm going to give you a hint so that you can continue working on this question.

    The prompt DOES NOT tell us that the triangle is a right triangle. NEITHER does Fact 1. You're assuming that it's a right triangle, BUT is it POSSIBLE that it's not?

    GMAT assassins aren't born, they're made,
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    Thanked by: phanikpk
    Post Thu Jun 26, 2014 8:55 am
    Quote:
    If the area of triangular region RST is 25. What is the perimeter of RST?
    1) THe length of one of the sides is 5(2)^1/2
    2) The triangle is a right isosceles triangle
    Statement 1:
    Case 1: 5(Sqrt2) is Height of a right angle triangle
    other Sides will be 5(sqrt2) and 10 leading to perimeter = 10 + 10(sqrt2)

    Case 2: 5(Sqrt2) is Height of a NON-right angle triangle with base 5(sqrt2)
    Three sides will NOT be 5(sqrt2),5(sqrt2) and 10 leading to perimeter something other than 10 + 10sqrt2

    Inconsistent result therefore, INSUFFICIENT STATEMENT

    Statement 2: The Isosceles right angle triangle with area 25 will essentially have sides as 5(sqrt2),5(sqrt2) and 10 therefore perimeter = 10+2x5sqrt2 = 10(1+sqrt2)

    SUFFICIENT

    Answer Option : B

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    Post Fri Jun 27, 2014 5:38 pm
    phanikpk wrote:
    If the area of triangular region RST is 25. What is the perimeter of RST?

    1) The length of one of the sides is 5√2
    2) The triangle is a right isosceles triangle

    VERY IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in our free video: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1103

    This technique can save a lot of time.

    Target question: What is the perimeter of RST?

    Given: The area of triangular region RST is 25.

    Statement 1: The length of one of the sides is 5√2
    There are several possible triangles such that the length of one side is 5√2. Here are two:

    Notice that the perimeter for each triangle is DIFFERENT. In other words, statement 1 does not lock our shape into having just one perimeter.
    As such, statement 1 is NOT SUFFICIENT

    Statement 2: The triangle is a right isosceles triangle
    This fact alone forces the triangle into having a 90-degree angle, 2 equal angles and 2 equal sides. Of course there still many different triangles (with different perimeters) that meet these conditions:

    HOWEVER, it is given that the area of the triangle is 25. Among the infinite number of isosceles right triangles, ONLY ONE has an area of 25.
    So, statement 2 (along with the given information) "locks" our triangle into ONE and ONLY ONE shape, which means there's only one possible perimeter.
    As such, statement 2 is SUFFICIENT.
    IMPORTANT: Need we actually find the perimeter of this triangle? No. We need only recognize that we COULD find the perimeter (if we so inclined to do so)

    Answer = B

    Cheers,
    Brent

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    Thanked by: phanikpk
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