Practice problem

Area and Perimeter of Dilated Figures

Mosaics and arabesques on a wall of the Myrtle court, Alhambra, Granada, Spain $\\$ Image by Jebulon via Wikimedia Commons (Creative Commons CC0 for Commercial Reuse)

Above is a picture of the famed Arabian palace in Spain: The Alhambra. It is well known for it's intricate geometric patterns. $\\$

Observe the image above. If the areas of the small, light blue rhombuses are $3\text{cm}^{2}$ , what is the side length of the larger areas outlined by the darker, black rhombuses? $\\$ Assume the white lines do not add a significant amount of area. $\\$ Assume the interior angles of the rhombuses are right angles.