Given: right-angled △ABC, the length of the hypotenuse c=5 and the sum of the legs a+b=6. Find the area of the triangle.
I tried creating the following system a+b=6;a2+b2=25 however it got me nowhere, I get a really ugly quadratic equation .
Answer
We have
Area =12absin∠C=12absinπ2=12ab=14[(a+b)2−(a2+b2)]=14(36−25)=114
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