RTriangle 17

The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm, you will reduce the hypotenuse by 4 cm. Determine the length of these legs.

Correct answer:

a =  15 cm
b =  8 cm

Step-by-step explanation:

172=a2+b2 (17−4)2=(a−3)2+(b−3)2  289=a2+b2 169=a2−6a+9+b2−6b+9  289=a2+b2 151=a2+b2−6a−6b  151=289−6a−6b 138=6a+6b 23=a+b  289=a2+b2 289=a2+(23−a)2 289=a2+232−46a+a2 2a2−46a+240=0 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=15 cm b=8 cm

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