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# triangle

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Manager
Joined: 13 Apr 2006
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triangle [#permalink]  04 May 2006, 08:03

For right triangle RST, RS and RT are legs and RS+RT=12. ST is hypotenuse w/length of 10. What is the area of the triangle?
Manager
Joined: 13 Dec 2005
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let the arms be x and y respectively say x as base and y as height
so x +y =12 eqn 1

also its a right angle traingle so

x^2 +y^2 = 10^2 (since 10 is hyptoneous) eqn 2

but we know

(x+y)^2 = x^2 +y^2 +2*x*y
i.e 144 =100 +2xy

implies xy =22

area or right angle traingle = (1/2) * base * height
= (1/2) *x *y
= (1/2) *22
=11

Hope the above explanation was clear enough to comprehend.
Manager
Joined: 13 Apr 2006
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Thank you, you made it very easy. I was trying to work out a complex quadratic, forgetting that I could plug in 100.
Senior Manager
Joined: 29 Jun 2005
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Area of the triangle is RT*RS/2
RS^2+RT^2=100
RS^2+2RS*RT+RT^2=144
Subtract and get 2 RS*RT=44 RS*RT/2= 11
Manager
Joined: 27 Mar 2006
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Agree Area = 11
VP
Joined: 29 Apr 2003
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Agreed 11.. Nicely explained!
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