The sides

The sides of a right triangle form an arithmetic sequence. The hypotenuse is 24 cm long. Determine the remaining sides of the triangle.

Correct result:

a =  14.4 cm
b =  19.2 cm

Solution:

c=24 cm a=c2d b=cd c2=a2+b2  c2=(c2d)2+(cd)2  242=(242 d)2+(24d)2 5d2+144d576=0 5d2144d+576=0  a=5;b=144;c=576 D=b24ac=144245576=9216 D>0  d1,2=b±D2a=144±921610 d1,2=144±9610 d1,2=14.4±9.6 d1=24 d2=4.8   Factored form of the equation:  5(d24)(d4.8)=0  d=d2=4.8=245  a=c2 d=242 4.8=725=725 cm=14.4 cm

Our quadratic equation calculator calculates it.

b=a+d=14.4+4.8=965=19.2=965 cm=19.2 cm   Verifying Solution:  c1=a2+b2=14.42+19.22=24 cm b1=c1d=244.8=965=19.2 cm a1=b1d=19.24.8=725=14.4 cm



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