Area of triangle

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sushbis: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Wed Feb 27, 2008 6:01 pm; Thanked: 1 times; Followed by:1 members

Area of triangle

by sushbis » Tue Oct 04, 2011 11:25 pm

A right triangle is drawn, the opposite site of right angle is 10, sum of the sides next to right angle is 12.
What is the area of the triangle?

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 am; Thanked: 38 times; Followed by:1 members

by sl750 » Tue Oct 04, 2011 11:29 pm

a+b=12

a^2+b^2 = 100 (Pythagorean theorem)

a^2+b^2 = (a+b)^2 -2ab

144 -2ab = 100 or ab 22; Area of triangle = 1/2ab or 11

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Tue Oct 04, 2011 11:48 pm

sushbis wrote:A right triangle is drawn, the opposite site of right angle is 10, sum of the sides next to right angle is 12.
What is the area of the triangle?

Area of triangle = (1/2) * x * y = xy/2, where x = base, y = height
By Pythagoras Theorem, xÂ² + yÂ² = 10Â²
xÂ² + yÂ² = (x + y)Â² - 2xy
10Â² = 12Â² - 2xy
2xy = 44 or xy = 22
So, area of triangle = 22/2 = 11 sq units

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