A rite triangle has sides 9 meters squared and 16 meters squared find the area of a and the length of b

3 answers

It seems like there's a misunderstanding in the phrasing of your question. A right triangle's sides should be lengths (in meters) rather than squared (in square meters).

Let's assume you meant that the lengths of the legs of the right triangle are 9 meters and 16 meters.

Step 1: Find the area of the triangle.

The area \( A \) of a right triangle can be calculated using the formula:

\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]

Here, we can take the two legs of the triangle as the base and height:

\[ A = \frac{1}{2} \times 9 , \text{m} \times 16 , \text{m} \] \[ A = \frac{1}{2} \times 144 , \text{m}^2 \] \[ A = 72 , \text{m}^2 \]

So, the area of the triangle is \( 72 , \text{m}^2 \).

Step 2: Find the length of the hypotenuse \( c \).

To find the length of the hypotenuse \( c \), we can use the Pythagorean Theorem:

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

Let \( a = 9 , \text{m} \) and \( b = 16 , \text{m} \):

\[ c^2 = 9^2 + 16^2 \] \[ c^2 = 81 + 256 \] \[ c^2 = 337 \] \[ c = \sqrt{337} \approx 18.36 , \text{m} \]

Summary:

  • The area of the triangle is \( 72 , \text{m}^2 \).
  • The length of the hypotenuse \( c \) is approximately \( 18.36 , \text{m} \).

If you meant something different, please clarify!

is it 7 and 5

It seems like you are asking about a different right triangle with sides of lengths 5 meters and 7 meters. Let's calculate the area and the hypotenuse for this triangle.

Step 1: Find the area of the triangle.

The area \( A \) of a right triangle can be calculated using the formula:

\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]

Assuming the two legs of the triangle are 5 meters and 7 meters:

\[ A = \frac{1}{2} \times 5 , \text{m} \times 7 , \text{m} \] \[ A = \frac{1}{2} \times 35 , \text{m}^2 \] \[ A = 17.5 , \text{m}^2 \]

So, the area of the triangle is \( 17.5 , \text{m}^2 \).

Step 2: Find the length of the hypotenuse \( c \).

To find the length of the hypotenuse \( c \), we can use the Pythagorean Theorem:

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

Where \( a = 5 , \text{m} \) and \( b = 7 , \text{m} \):

\[ c^2 = 5^2 + 7^2 \] \[ c^2 = 25 + 49 \] \[ c^2 = 74 \] \[ c = \sqrt{74} \approx 8.6 , \text{m} \]

Summary:

  • The area of the triangle with sides of 5 meters and 7 meters is \( 17.5 , \text{m}^2 \).
  • The length of the hypotenuse \( c \) is approximately \( 8.6 , \text{m} \).

If you had something else in mind or if you meant different values, please let me know!