Rhombus

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

The perimeter of a rhombus is 56 cm, and one of the diagonals is of length 14 cm.

Final Answer:

d₂ =  24.25 cm
S =  169.74 cm²

Step-by-step explanation:

$$\begin{gathered} p=56\text{cm} \\ {d}_1=14\text{cm} \\ p=4a \\ p=2\sqrt{d_1^2+d_2^2} \\ {d}_2=\sqrt{\frac{p^2}{4}-d_1^2}=\sqrt{\frac{56^2}{4}-14^2}=14\sqrt{3}=24.25\text{cm} \end{gathered}$$

$S=\frac{d_1\cdot d_2}{2}=\frac{14\cdot 24.2487}{2}=98\sqrt{3}=169.74{\text{cm}}^2$

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