Triangle Problem Help

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EMAN: Master | Next Rank: 500 Posts; Posts: 162; Joined: Sun Aug 09, 2009 4:17 pm; Location: Minnesota; Thanked: 1 times

Triangle Problem Help

by EMAN » Sun Oct 04, 2009 3:27 pm

The hypotenuse of a right triangle is 10 cm. What is the perimeter, in cm, of the triangle?

(1) The area of the triangle is 25 cm squared
(2) The 2 legs of the triangle are equal in length

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Source: Beat The GMAT — Data Sufficiency | Sun Oct 04, 2009 3:27 pm

kholll557MBA10: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sun Oct 04, 2009 4:38 pm

Re: Triangle Problem Help

by kholll557MBA10 » Sun Oct 04, 2009 5:10 pm

Did you not figure out the other 2 sides? I know that the equation for the area of a triangle is 1/2bh since the area is 25 we know that the (bh) has to equal 50,in order for the area to be 25.. since number (2) says that 2 of the legs are equal and we know the hypotenuse is 10, what times what will equal 50, 1*50, 2*25, 5*10. so the answer would have to be 10*5, so the sides of the triangle are 10, 10, 5, which means the perimeter is 25.

EMAN wrote:The hypotenuse of a right triangle is 10 cm. What is the perimeter, in cm, of the triangle?

(1) The area of the triangle is 25 cm squared
(2) The 2 legs of the triangle are equal in length

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umaa: Legendary Member; Posts: 727; Joined: Sun Jun 08, 2008 9:32 pm; Thanked: 8 times; Followed by:1 members

Re: Triangle Problem Help

by umaa » Sun Oct 04, 2009 5:23 pm

EMAN wrote:The hypotenuse of a right triangle is 10 cm. What is the perimeter, in cm, of the triangle?

(1) The area of the triangle is 25 cm squared
(2) The 2 legs of the triangle are equal in length

IMO D.

Since its a right angle triangle, we can use Pythagoras theorm.

sqrroot (a^2 + b^2) = 10

a^2 + b^2 = 100 - I

Statement 1:
Area of the triangle ab/2 = 25

ab = 50; 2ab = 100

Combine this equation with equation I,

a^2 + b^2 + 2ab = 100+100

(a+b)^2 = 200
a+b = sqrrot(200)

Since we already know c(diagonal), a+b+c = sqrrot(200)+10

So, Statement 1 is sufficient.

Statement 2:
If 2 legs of the triangle is equal, we are sure that hypotenuse is not one of the length. It should be a and b.

If both are equal, then the angle is 45:45:90.

From there, we can find a+b+c

Statement 2 is also sufficient.

OA pls.

What we think, we become

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EMAN: Master | Next Rank: 500 Posts; Posts: 162; Joined: Sun Aug 09, 2009 4:17 pm; Location: Minnesota; Thanked: 1 times

Correct

by EMAN » Sun Oct 04, 2009 6:23 pm

I believe you are correct. I don't have the books in front of me though. Can you explain the 2ab part of the equation? I think they mentioned that in the OG and I was a little thrown off by that.

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umaa: Legendary Member; Posts: 727; Joined: Sun Jun 08, 2008 9:32 pm; Thanked: 8 times; Followed by:1 members

by umaa » Sun Oct 04, 2009 6:28 pm

We know the hypotenuse. Its 10. The triangle is right angle triangle. it means, one angle is 90 degree. hypotenuse is opposite to 90 degree.

If the other 2 sides are equal, then it means, the other two angles are equal.

180-90 =90; 90/2 = 45

So, both the angles are 45:45.

We know 45:45:90 measurements. its, x