Rhombus and inscribed circle

It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.

Correct answer:

u =  11.2101 cm
v =  4.2819 cm

Step-by-step explanation:

a=6 cm r=2 cm  a=a1+a2 r2=a1a2 a1(aa1)=r2  x(6x)=22  x(6x)=22 x2+6x4=0 x26x+4=0  a=1;b=6;c=4 D=b24ac=62414=20 D>0  x1,2=2ab±D=26±20=26±25 x1,2=3±2.2360679774998 x1=5.2360679774998 x2=0.76393202250021   Factored form of the equation:  (x5.2360679774998)(x0.76393202250021)=0  a1=x1=5.23615.2361 a2=x2=0.76390.7639  (u/2)2=a12+r2 u=2 a12+r2=2 5.23612+22=11.2101 cm

Our quadratic equation calculator calculates it.

(v/2)2=a22+r2 v=2 a22+r2=2 0.76392+224.2819 cm  r2=a1 a2=5.2361 0.7639=2 r2=r

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