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.

Result

u =  11.21 cm
v =  4.282 cm

Solution:


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(v/2)2=a22+r2 v=2⋅ a22+r2=2⋅ 0.76392+22≐4.2819≐4.282 cm  r2=a1⋅ a2=5.2361⋅ 0.7639=2 r2=r(v/2)^2=a_{2}^2 + r^2 \ \\ v=2 \cdot \ \sqrt{ a_{2}^2 + r^2 }=2 \cdot \ \sqrt{ 0.7639^2 + 2^2 } \doteq 4.2819 \doteq 4.282 \ \text{cm} \ \\ \ \\ r_{2}=\sqrt{ a_{1} \cdot \ a_{2} }=\sqrt{ 5.2361 \cdot \ 0.7639 }=2 \ \\ r_{2}=r

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The diagonal of a rhombus measure 16cm and 30cm find its perimeter

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