The area of the red square is 16 ft^(2)

Question

. The area of the yellow square is 25 ft^(2)
.
The image illustrates the Pythagorean theorem, showing a right triangle with squares constructed on each of its sides. The triangle's sides are labeled a, b, and c, where c is the hypotenuse. The squares on the sides a, b, and c are colored green, red, and yellow, respectively. This visual representation demonstrates the theorem, which states that the area of the square on the hypotenuse (c²) is equal to the sum of the areas of the squares on the other two sides (a² + b²). In other words, the area of the yellow square is equal to the sum of the areas of the green and red squares.
What is the area of the green square?
Responses
A 3 ft^(2)
B 9 ft 2
C 81 ft 2
D 128 ft 2
E 256 ft^(2)

Answer 1

To find the area of the green square, we use the Pythagorean theorem, which states that the area of the square on the hypotenuse (c²) is equal to the sum of the areas of the squares on the other two sides (a² + b²).

Given:

• Area of the red square (a²) = 16 ft²
• Area of the yellow square (c²) = 25 ft²

According to the Pythagorean theorem: \[ c² = a² + b² \] Plugging in the values we have: \[ 25 = 16 + b² \]

Now, solve for b² (the area of the green square): \[ b² = 25 - 16 \] \[ b² = 9 \]

Therefore, the area of the green square is \( 9 , \text{ft}² \).

The correct answer is: B 9 ft²