Question

Find the area of the missing square off of leg a if the area of one square is 369 and the area of another is 81.

Answer 1

Solution:

Note that:

• Area of square = s² (s = Side length)

Finding the leg of a square with area of 369 units²

• c² = 369
• => c = √369 units

Finding the leg of a square with area of 81 units²

• b² = 81
• => b = √81 = 9 units

Finding side length a using Pythagoras theorem

• (√369)² = 9² + a²
• => 369 = 81 + a²
• => 369 - 81 = a²
• => 288 = a²
• => a = √288 = √144 x 2 = √12 x 12 x 2 = 12√2 units

Finding the missing area of the square.

• Area of square = a²
• => Area of square = a² = (a)²
• => Area of square = (12√2)²
• => Area of square = (12√2)(12√2) = 288 units²

Option D is correct.