Rhombus

Find the length of the other diagonal and area of rhombus.

The perimeter of a rhombus is 40 cm and one of the diagonals is of length 10 cm.

Result

d2 =  17.32 cm
S =  86.6 cm2

Solution:

p=2d12+d22 40=2102+d22 d2=4024−102=17.32 cmp = 2 \sqrt{ d_1^2 + d_2^2 } \ \\ 40 = 2 \sqrt{ 10^2 + d_2^2 } \ \\ d_2 = \sqrt{ \dfrac{ 40^2}{4} - 10^2 } = 17.32 \ \text{cm}
S=d1d22=86.6 cm2S = \dfrac{ d_1 d_2 }{2} = 86.6 \ \text{cm}^2

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