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=24011681 2a(49a)=720 249a2a2=720  2a298a+720=0 2 ...  prime number 98=272 720=24325 GCD(2,98,720)=2=2  a249a+360=0  p=1;q=49;r=360 D=q24pr=49241360=961 D>0  a1,2=2pq±D=249±961 a1,2=249±31 a1,2=24.5±15.5 a1=40 a2=9   Factored form of the equation:  (a40)(a9)=0 

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