Answer:The length of the third side is √73Step-by-step explanation:To find the third side, we use the Pythagorean Theorem: a² + b² = c²a² and b² are the two smaller sides c² is the longest sideThe two shortest sides are 4√2 and ?The longest side is 9a² = 4√2²b² = ?c² = 9²Now we put together the equation:4(√2)² + b² = 9²The square of √2 is 24 × 2 + b² = 9²Multiply 4 and 2 to get 88 + b² = 9²Calculate 9 to the power of 2 and get 818 + b² = 81Subtract 8 from both sides8 + b² - 8 = 81 - 8Subtract 8 from 81 to get 73b² = 73Take the square root of both sides of the equation√b² = √73Simplifyb = √73Length of third side: √73Answer in decimal form: 8.5440037453175311678716483262397