Question

find the length of the diagonal of a rhombus (the rhombus is shown in the image with some segment lengths marked, like 25, 28, etc.)

Explanation:

Step1: Identify rhombus side length

Use half-diagonals: $\frac{20}{2}=10$, $\frac{28}{2}=14$. Side $s=\sqrt{10^2+14^2}$

Step2: Calculate side length

$ s=\sqrt{100+196}=\sqrt{296}=\sqrt{4\times74}=2\sqrt{74} $

Step3: Find perimeter of rhombus

Perimeter $P=4s$

Step4: Compute final perimeter

$ P=4\times2\sqrt{74}=8\sqrt{74} $

Answer:

$8\sqrt{74}$