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 (c−4)2=(a−3)2+(b−3)2=(17−4)2=169  169=a2−2⋅3a+32+b2−2⋅3b+32 169=a2+b2−6⋅a−6⋅b+18 169−289−18=−6⋅a−6⋅b  b=−a−(−23)  c2=289=a2+(−a−(−23))2 2a2−46a+240=0 2 ...  prime number 46=2⋅23 240=24⋅3⋅5 GCD(2,46,240)=2=2  a2−23a+120=0  p=1;q=−23;r=120 D=q2−4pr=232−4⋅1⋅120=49 D>0  a1,2​=2p−q±D​​=223±49​​ a1,2​=223±7​ a1,2​=11.5±3.5 a1​=15 a2​=8   Factored form of the equation:  (a−15)(a−8)=0  a=a1​=15 cm b=a2​=8 cm

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