Question

The side of a rhombus is $5$ cm. If the length of one diagonal of the rhombus is $8$ cm, then find length of the other diagonal.

Answer 1

The diagonals of a rhombus intersect at the right angle.

half of each diagonal and the length of the side will form as a right-angle triangle.

Diagonal $=8$ cm.

$\frac{1}{2}$ of the diagonal $=\frac{8}{2}=4$ cm

$\therefore a^2+b^2=c^2$

$\Rightarrow a^2+4^2=5^2$

$\Rightarrow a^2-25=16$

$\Rightarrow a^2=9$

$\Rightarrow a=\sqrt{9}$

$\Rightarrow a=3.$

Length of the diagonal

$\frac{1}{2}$ of the diagonal $=3$ cm

the diagonal $=3\times 2=6$ cm

$\therefore$ The length of the other diagonal is $6$ cm.