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 (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 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=15 cm b=8 cm

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