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