Question

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

Answer 1

is it 7 and 5

Answer 2

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!

Answer 3

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!