To solve the problem, we interpret the right triangle (b) as having legs or "outer sides" of lengths 9 meters and 16 meters.
Step 1: Calculate the area of the right triangle (b)
The area \( A \) of a right triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Assuming that the lengths of the legs of the triangle are 9 meters and 16 meters:
\[ A = \frac{1}{2} \times 9 \times 16 = \frac{1}{2} \times 144 = 72 \text{ m}^2 \]
Step 2: Calculate the length of (b)
The length of the hypotenuse \( c \) of the right triangle can be found using the Pythagorean theorem:
\[ c = \sqrt{a^2 + b^2} \]
Where \( a \) and \( b \) are the lengths of the two legs. In this case:
\[ c = \sqrt{9^2 + 16^2} = \sqrt{81 + 256} = \sqrt{337} \approx 18.36 \text{ m} \]
Step 3: Calculate the area of the square (a)
Let's denote the side length of the square (a) as \( s \). If the square is adjacent to the right triangle (b), its side length could be equal to one of the legs of the triangle. Assuming that the square's side is equal to the leg measuring 9m (this can vary depending on how they are placed), the area \( A_s \) of the square can be calculated as:
\[ A_s = s^2 \]
If we take \( s = 9 \) meters:
\[ A_s = 9^2 = 81 \text{ m}^2 \]
Summary of Results
- Area of right triangle (b): 72 m²
- Length of hypotenuse (b): ≈ 18.36 m
- Area of square (a): 81 m² (assuming the side length equals 9 m)
To finalize, the exact area of the square may vary depending on its side length. If the square side is assumed differently, simply replace 9 with the new side length to find the area.
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