Question

if the perimeter of a rhombus is 8√5 and one diagonal has the length of 4√2, find the length of the other diagonal

Answer 1

Perimeter = 4 l

$\begin{gathered} \text{ l = 2}\sqrt[]{5} \\ \text{Diagonal = 4}\sqrt[]{2} \end{gathered}$

Pytagorean theorem

$\begin{gathered} \text{ l}^2-d^2\text{ = second diagonal} \\ \sec onddiagonal^2\text{= (2}\sqrt[]{5})^2\text{ - (2}\sqrt[]{2})^2 \\ seconddiagonal^2\text{ = 4(5) - 4(2)} \\ seconddiagonal^2\text{ = 20 - 8} \\ ddiagonal^2\text{ = 12} \\ \text{second diagonal = }\sqrt[]{12}\text{ = 2}\sqrt[]{3} \\ \text{second diagonal = 2}\sqrt[]{3} \end{gathered}$