Question

the diagonal of a rhombus are 14 inches and 28 inches. What is the perimeter of the rhombus in inches. draw a picture

Answer 1

The diagonal of rhombus is:

$\begin{gathered} d_2=\sqrt[]{4a^2-d^2_1} \\ d^2_2=4a^2-d^2_1 \\ d^2_1+d^2_2=4a^2 \end{gathered}$

so side of rombus (a) is:

$\begin{gathered} 14^2+28^2=4a^2 \\ 196+784=4a^2 \\ \frac{980}{4}=a^2 \\ a^2=245 \\ a=\sqrt[]{245} \\ a=15.65247 \end{gathered}$

Perimeter of rombus is:

$\begin{gathered} \text{Perimeter}=4a \\ =4\times15.65247 \\ =62.609 \end{gathered}$