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 (AB) = 8 m
- Width (BC) = 6 m

### Step 2: Understand the relationship in the rectangle
In a rectangle, the diagonal (AC) divides it into two right-angled triangles. According to the Pythagorean theorem, the square of the length of the diagonal is equal to the sum of the squares of the lengths of the two sides.

### Step 3: Apply the Pythagorean theorem
Using the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]

Substituting the values:
\[ AC^2 = (8 \, m)^2 + (6 \, m)^2 \]

### Step 4: Calculate the squares of the sides
Calculating the squares:
\[ AC^2 = 64 + 36 \]

### Step 5: Add the squares
Now, add the results:
\[ AC^2 = 100 \]

### Step 6: Find the length of the diagonal
To find AC, take the square root of both sides:
\[ AC = \sqrt{100} \]
\[ AC = 10 \, m \]

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

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