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# triangle

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Manager
Joined: 13 Apr 2006
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04 May 2006, 09:03
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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?

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Manager
Joined: 13 Dec 2005
Posts: 224

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Location: Milwaukee,WI

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04 May 2006, 09:13
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.

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Manager
Joined: 13 Apr 2006
Posts: 56

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04 May 2006, 09:20
Thank you, you made it very easy. I was trying to work out a complex quadratic, forgetting that I could plug in 100.

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Senior Manager
Joined: 29 Jun 2005
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05 May 2006, 04:03
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

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Manager
Joined: 27 Mar 2006
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07 May 2006, 14:22
Agree Area = 11

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VP
Joined: 29 Apr 2003
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08 May 2006, 03:53
Agreed 11.. Nicely explained!

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08 May 2006, 03:53
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# triangle

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