The area of the green square is 9 ft^(2)

Question

. The area of the red square is 16 ft^(2)
The image depicts a visual representation of the Pythagorean Theorem. It features a right-angled triangle with sides labeled 'a', 'b', and 'c', where 'c' is the hypotenuse. Attached to each side of the triangle is a square, with the square on side 'a' colored green, the square on side 'b' colored red, and the square on side 'c' colored yellow. This arrangement visually demonstrates the theorem, which states that the area of the square built upon the hypotenuse (c) of a right triangle is equal to the sum of the areas of the squares on the other two sides (a and b). The equation of the Pythagorean Theorem is a²+b²=c².

What is the area of the yellow square?
Responses
A 25
25 ft 2
B 49
49 ft 2
C 81
81 ft 2
D 128
128 ft 2
E 256

Answer 1

To find the area of the yellow square (which corresponds to the hypotenuse 'c'), we can use the Pythagorean Theorem:

\[ a^2 + b^2 = c^2 \]

From the information given:

• The area of the green square (side 'a') is \(9 , \text{ft}^2\), so: \[ a^2 = 9 \implies a = \sqrt{9} = 3 , \text{ft} \]

• The area of the red square (side 'b') is \(16 , \text{ft}^2\), so: \[ b^2 = 16 \implies b = \sqrt{16} = 4 , \text{ft} \]

Now substituting the values of \(a\) and \(b\) into the Pythagorean theorem:

\[ c^2 = a^2 + b^2 = 9 + 16 = 25 \]

Therefore, the area of the yellow square \(c^2\) is:

\[ c^2 = 25 , \text{ft}^2 \]

The correct response is:

A 25 ft²