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=24011681 2a(49a)=720 249a2a2=720  2a298a+720=0  p=2;q=98;r=720 D=q24pr=98242720=3844 D>0  a1,2=2pq±D=498±3844 a1,2=498±62 a1,2=24.5±15.5 a1=40 a2=9   Factored form of the equation:  2(a40)(a9)=0 
b=a2=9



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