The area of a rectangle is 112. The length is 7, and the width is $$ \sqrt{x} $$. What is the value of x? What is the width of the rectangle?

To solve for the value of $ x $ and the width of the rectangle, we can use the given information and the formula for the area of a rectangle:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

Given:
- Area = 112
- Length = 7
- Width = $ \sqrt{x} $

Substituting the known values into the area formula:

\[
112 = 7 \times \sqrt{x}
\]

Now, solve for $ \sqrt{x} $:

\[
\sqrt{x} = \frac{112}{7} = 16
\]

Next, to find $ x $, square both sides of the equation:

\[
x = 16^2 = 256
\]

So, the value of $ x $ is $ 256 $.

Finally, the width of the rectangle is $ \sqrt{x} $:

\[
\text{Width} = \sqrt{256} = 16
\]

### Summary:
- The value of $ x $ is $ 256 $.
- The width of the rectangle is $ 16 $.

Would you like more details or have any questions?

Here are some related questions:
1. What is the relationship between the length, width, and area of other polygons?
2. How would the width change if the area of the rectangle were doubled?
3. What is the perimeter of this rectangle?
4. How do you find the diagonal of the rectangle using $ x $?
5. How would you solve for $ x $ if the length were given as $ \sqrt{x} $ and the width as 7?

**Tip:** When dealing with square roots in equations, remember to square both sides to eliminate the square root and simplify the equation.

The area of a rectangle is 112. The length is 7, and the width is $ \sqrt{x} $. What is the value of x? What is the width of the rectangle?

This problem explores finding the value of x and the width of a rectangle with an area of 112, length 7, and width $ \sqrt{x} $. Learn how to apply basic algebra and geometry to solve for square roots and rectangle dimensions. Suitable for Grades 6-8.

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