The squared value of the diagonal of a rectangle `(64 + x^2)` sq. cm. where x is less than 8 cm. what is the length of that rectangle ?

Options

A. 6 cms
B. 10 cms
C. 8 cms
D. Data inadequate

Answer

To solve the problem, we need to find the length of the rectangle given that the squared value of the diagonal is \(64 + x^2\) square centimeters, where \(x\) is less than 8 cm.

### Step-by-step Solution:

1. **Understand the relationship between the sides of the rectangle and the diagonal**:
The diagonal \(d\) of a rectangle can be calculated using the Pythagorean theorem:
\[ d^2 = l^2 + b^2 \]
where \(l\) is the length and \(b\) is the breadth of the rectangle.

2. **Set up the equation using the given information**:
We are given that:
\[ d^2 = 64 + x^2 \]
Therefore, we can equate this to the Pythagorean theorem:
\[ l^2 + b^2 = 64 + x^2 \]

3. **Analyze the information provided**:
We have one equation but two unknowns (length \(l\) and breadth \(b\)). Without additional information about either the length or the breadth, we cannot uniquely determine the length of the rectangle.

4. **Conclusion**:
Since we do not have enough information to find the length of the rectangle, we conclude that the data is inadequate to solve for the length.

### Final Answer:
The data is inadequate to determine the length of the rectangle.