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 this legs.

Correct answer:

a =  15 cm
b =  8 cm

Step-by-step explanation:

172=a2+b2 (174)2=(a3)2+(b3)2  289=a2+b2 169=a26a+9+b26b+9  289=a2+b2 151=a2+b26a6b  151=2896a6b 138=6a+6b 23=a+b  289=a2+b2 289=a2+(23a)2 289=a2+23246a+a2 2a246a+240=0 2a246a+240=0  p=2;q=46;r=240 D=q24pr=46242240=196 D>0  a1,2=2pq±D=446±196 a1,2=446±14 a1,2=11.5±3.5 a1=15 a2=8   Factored form of the equation:  2(a15)(a8)=0   a=15 cm b=8 cm

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