Catheti

The hypotenuse of a right triangle is 41, and the sum of legs is 49. Calculate the length of its legs.

Correct answer:

a =  40
b =  9

Step-by-step explanation:

c=41 a+b=49 a2+b2=c2=1681 (a+b)2=492 a2+2ab+b2=2401  2ab=2401−1681 2a(49−a)=720 2⋅49a−2a2=720  2a2−98a+720=0 2 ...  prime number 98=2⋅72 720=24⋅32⋅5 GCD(2,98,720)=2=2  a2−49a+360=0  p=1;q=−49;r=360 D=q2−4pr=492−4⋅1⋅360=961 D>0  a1,2​=2p−q±D​​=249±961​​ a1,2​=249±31​ a1,2​=24.5±15.5 a1​=40 a2​=9   Factored form of the equation:  (a−40)(a−9)=0 
b=a2​=9

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