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2015-10-02T10:33:33+05:30

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Side of rhombus, a = 10cm
one of the diagonal, d₁ = 12cm
length of other diagonal = d₂

 (\frac{d_1}{2} )^2+ (\frac{d_2}{2} )^2 = a^2\\ \\ \Rightarrow  (\frac{12}{2} )^2+ (\frac{d_2}{2} )^2 = 10^2\\ \\ \Rightarrow 6^2 + (\frac{d_2}{2} )^2 = 100\\ \\ \Rightarrow (\frac{d_2}{2})^2 = 100-36=64\\ \\ \Rightarrow \frac{d_2}{2}= \sqrt{64}=8\\ \\ \Rightarrow d_2=2 \times 8=\boxed{16\ cm}

Other length of diagonal is 16cm.
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2015-10-02T13:05:05+05:30

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Half a diagonal will be the height of the right angled triangle formed, so :

\sqrt{10^2-6^2}=x
\sqrt{100-36}=x
\sqrt{63}=x
8=x
x=8

Now half a diagonal (the other one) is 8.
Therefore the whole diagonal is 2 × 2 × 2 × 2 = 16.

Ans: 16cm



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