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What is the perimeter?

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What is the perimeter?

by phanikpk » Wed Jun 25, 2014 3:17 pm
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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Source: — Data Sufficiency |

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by [email protected] » 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?

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by GMATinsight » Thu Jun 26, 2014 8:55 am
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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by Brent@GMATPrepNow » 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: https://www.gmatprepnow.com/module/gmat- ... cy?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:
Image
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:
Image
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
Brent Hanneson - Creator of GMATPrepNow.com
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