find the length of the diagonal of a rectangle whose sides are 8 m and 6m.

Answer

To find the length of the diagonal of a rectangle with sides measuring 8 m and 6 m, we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Identify the sides of the rectangle
Let the lengths of the sides of the rectangle be:
- Length (AD) = 8 m
- Width (DC) = 6 m

### Step 2: Understand the relationship in the rectangle
In a rectangle, the diagonal (AC) forms a right triangle with the two sides (AD and DC). Therefore, we can apply the Pythagorean theorem.

### Step 3: Apply the Pythagorean theorem
According to the Pythagorean theorem:
\[ AC^2 = AD^2 + DC^2 \]

### Step 4: Substitute the values
Substituting the values of the sides into the equation:
\[ AC^2 = 8^2 + 6^2 \]

### Step 5: Calculate the squares
Calculating the squares:
\[ AC^2 = 64 + 36 \]

### Step 6: Add the results
Adding the results:
\[ AC^2 = 100 \]

### Step 7: Take the square root
To find AC, take the square root of both sides:
\[ AC = \sqrt{100} \]

### Step 8: Simplify the square root
Calculating the square root gives:
\[ AC = 10 \, \text{m} \]

### Final Answer
The length of the diagonal of the rectangle is **10 m**.

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