Right angled triangle

Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs.

Correct result:

a =  15 cm
b =  8 cm

Solution:

c2=a2+b2=172=289 (c4)2=(a3)2+(b3)2=(174)2=169  169=a223a+32+b223b+32 169=a2+b26a6b+18 16928918=6a6b  b=a(23)  c2=289=a2+(a(23))2 2a246a+240=0  p=2;q=46;r=240 D=q24pr=46242240=196 D>0  a1,2=q±D2p=46±1964 a1,2=46±144 a1,2=11.5±3.5 a1=15 a2=8   Factored form of the equation:  2(a15)(a8)=0  a=a1=15 cm b=a2=8 cm

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