Question

the side of a rombus is 10cm and length of one diagonal is 12cm . find the other
length of the diogonal???

Answer 1

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.

Answer 2

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