Catheti

The hypotenuse of a right triangle is 35, and the sum of legs is 49. Calculate the length of its legs.

Final Answer:

a =  28
b =  21

Step-by-step explanation:

c= 35 a+b = 49 a2 + b2 = c2 = 1225 (a+b)2 = 492 a2+2ab+b2 = 2401  2ab = 24011225 2a(49a)=1176  2a2+98a1176=0 2a298a+1176=0 2 ...  prime number 98=272 1176=23372 GCD(2,98,1176)=2  a249a+588=0  p=1;q=49;r=588 D=q24pr=49241588=49 D>0  a1,2=2pq±D=249±49 a1,2=249±7 a1,2=24.5±3.5 a1=28 a2=21  a=a1=28

Our quadratic equation calculator calculates it.

b=a2=21   Verifying Solution:  c2=a2+b2=282+212=35 s2=a+b=28+21=49



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