The adjacent sides of a rectangle are 7 cm and 24 cm . Find the length of its diagonal.

Answer

To find the length of the diagonal of a rectangle with adjacent sides measuring 7 cm and 24 cm, 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 adjacent sides of the rectangle be:
- Side AB = 7 cm
- Side BC = 24 cm

### Step 2: Apply the Pythagorean theorem
In a rectangle, the diagonal (AC) can be found using the Pythagorean theorem, which states:
\[ AC^2 = AB^2 + BC^2 \]
where:
- \( AC \) is the length of the diagonal,
- \( AB \) is one side (7 cm),
- \( BC \) is the other side (24 cm).

### Step 3: Substitute the values into the equation
Now, substituting the values we have:
\[ AC^2 = 7^2 + 24^2 \]

### Step 4: Calculate the squares
Calculating the squares:
- \( 7^2 = 49 \)
- \( 24^2 = 576 \)

Now, substitute these values back into the equation:
\[ AC^2 = 49 + 576 \]

### Step 5: Add the results
Now, add the two results:
\[ AC^2 = 625 \]

### Step 6: Take the square root
To find \( AC \), take the square root of both sides:
\[ AC = \sqrt{625} \]

### Step 7: Calculate the square root
Calculating the square root gives:
\[ AC = 25 \, \text{cm} \]

### Final Answer
Thus, the length of the diagonal of the rectangle is **25 cm**.

---