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24. If the area of triangular region RST is 25, what is the perimeter of RST? (1) The length of one side of RST is 5 sqrt 2. (2) RST is a right isosceles triangle.

(1) The length of one side is given . but no information abt other sides. Insufficient (2)The triangle is right isosceles let one side be x So area=1/2 *base*height=25. here base=height (isoscels triagle)=x Therefore, 1/2 *x*x=25 so x can be found since right triangle so third side can be found say y Perimeter is 2x+y So sufficient Hence answer is B

The question stem tells us that 1/2 * b * h = 25 and asks us to determine what RS + ST + TR is.

(1) Statement just tells us what one of the 3 sides is where the b and h could still take several values and affect the other two sides:

Insufficient

(2) This statement simply tells us that b = h so b^2 = 50. If we know the lengths of two sides of a right triangle, then we can determine (I won't calculate it here since it would be a waste of time on test day) the length of the other. So:

the answer should be B since in a right isosceles triangle, base = height and area is (base*height)/2 - so we can get both the sides and then hypotenuse is side*sqrt 2 - so I am a bit surprised that the answer is C - it is anyway not A and D. E is also out of the question.

I think C is right..how do we know from B which side is base?

i mean i could have a 90-degree-45-45 isso triangle and it will have perimeter of 10+5+5=20..

i could have a different isso triangle..

hi fresinha12, is it required to know whats the base??? in any case let what ever be the base the area will be same

I agree with Rohit, you can change the position but the relative sides will be the same hence you can trace a perpendicular for the height wherever you want and you would still have the same area and same perimeter.

Hence for me (B) is the correct choce Let us know if this is the OA will you? Thanks Cheers J

If the area of triangular region RST is 25, what is the perimeter of RST?

(1) The length of one side of RST is \(5\sqrt{2}\). (2) RST is a right isosceles triangle.

I think C is right..how do we know from B which side is base?

i mean i could have a 90-degree-45-45 isso triangle and it will have perimeter of 10+5+5=20..

i could have a different isso triangle..

hi fresinha12, is it required to know whats the base??? in any case let what ever be the base the area will be same

I agree with Rohit, you can change the position but the relative sides will be the same hence you can trace a perpendicular for the height wherever you want and you would still have the same area and same perimeter.

Hence for me (B) is the correct choce Let us know if this is the OA will you? Thanks Cheers J

The correct answer is B. From (2) we know that 1/2*leg^2=25 --> we can get the length of the legs, and since it's a 45-45-90 right isosceles triangle, we can get the length of the hypotenuse too. _________________

Re: If the area of triangular region RST is 25, what is the [#permalink]

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09 Dec 2014, 15:42

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If the area of triangular region RST is 25, what is the [#permalink]

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15 Feb 2015, 03:00

So the prompt tells us that the area of a triangle is 25 or that b*h=50 we are looking for the perimeter

(I) doesn't really tell us anything. Giving us one side is useless because we have no idea what the other sides could be (II) actually tells us quite a lot. The fact that it is an isosceles right triangle tells us that b=h, so we know that those sides are rt(50) long and we can use that information to figure out the hypotenuse and add them up to get the perimeter. _________________

Re: If the area of triangular region RST is 25, what is the [#permalink]

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19 Oct 2015, 11:55

B. Statement 1- insufficient just says one side is 5 root 2 but no info about the other 2 sides is given Statement 2- sufficient .. Isosceles right angled triangle therefore 1/2*side^2=25 side^2=50 side =root 50 Therefore hypotenuse = 2* (5 root 2) = 10 Perimeter =. 2(root 50) + 10

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