Question

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then the length of the side of the rhombus is __________.

Answer 1

Let the length of the side of the rhombus be a cm.

We know

(Length of one diagonal of rhombus)² + (Length of other diagonal of rhombus)² = 4 × (Length of side of rhombus)²

$$\begin{gathered} \therefore 4a^2={\left(16\right)}^2+{\left(12\right)}^2 \\ \Rightarrow 4a^2=256+144 \\ \Rightarrow 4a^2=400 \end{gathered}$$
$$\begin{gathered} \Rightarrow a^2=100 \\ \Rightarrow a=10\mathrm{cm} \end{gathered}$$

Thus, the length of the side of the rhombus is 10 cm.

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then the length of the side of the rhombus is ___10 cm___.