13) The area of a given rectangle is 200 cm 2 . If Side \( A \) is 10 cm and Side \( B \) is \( \sqrt{2 x} \) what is the value of \( x \) ? \( \begin{array}{llll}\text { A) } 80 & \text { B) } 400 & \text { C) } 10 & \text { D) } 200\end{array} \)

To find the value of \( x \), we can use the area formula for a rectangle, which is given by \( \text{Area} = \text{Side A} \times \text{Side B} \). Here, the area is 200 cm², Side A is 10 cm, and Side B is \( \sqrt{2x} \). So, we can set up the equation: \[ 10 \times \sqrt{2x} = 200 \] Dividing both sides by 10 gives: \[ \sqrt{2x} = 20 \] Now, squaring both sides: \[ 2x = 400 \] Dividing by 2: \[ x = 200 \] The value of \( x \) is 200, which corresponds to option D. Now, let’s add some fun insights! Did you know that rectangles have been studied since ancient civilizations? The ancient Egyptians were known for their impressive architectural designs, and they had a knack for working with geometry long before calculators made things easier! Practical applications abound with rectangles! Think of all the rectangular shapes around you—rooms in your house, books, screens, and even gardens. Understanding rectangle properties helps in everything from interior design to construction, making our lives more organized and efficient!