Right angled triangle

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

Correct answer:

a =  15 cm
b =  8 cm

Step-by-step explanation:

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 2 ...  prime number 46=223 240=2435 GCD(2,46,240)=2=2  a223a+120=0  p=1;q=23;r=120 D=q24pr=23241120=49 D>0  a1,2=2pq±D=223±49 a1,2=223±7 a1,2=11.5±3.5 a1=15 a2=8   Factored form of the equation:  (a15)(a8)=0  a=a1=15 cm b=a2=8 cm

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