Rhombus

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

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

Correct answer:

d₂ =  17.32 cm
S =  86.6 cm²

Step-by-step explanation:

$$\begin{gathered} p=2\sqrt{d_1^2+d_2^2} \\ 40=2\sqrt{10^2+d_2^2} \\ {d}_2=\sqrt{{\displaystyle \frac{40^2}{4}}-10^2}=17.32\text{ cm} \end{gathered}$$

$S={\displaystyle \frac{d_1{d}_2}{2}}=86.6{\text{cm}}^2$

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