15. If a rectangle has a length that is equal to $$ \frac{5}{2} $$ of its width) and the area is $$ 250 \mathrm{in}^{2} $$ (2) what is its width? a. 625 in b. 25 in c. 100 in d. 10 in e. 125 in

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To determine the width of the rectangle, let's break down the information provided:

1. **Given:**
    - **Length (L)** is $$ \frac{5}{2} $$ times the **width (W)**.
    - **Area (A)** of the rectangle is $$ 250 \, \text{in}^2 $$.

2. **Formulate the Equation:**
    - The area of a rectangle is calculated as:
      $$
      A = L \times W
      $$
    - Substitute the given relationship between length and width into the area formula:
      $$
      250 = \left( \frac{5}{2} W \right) \times W
      $$
      $$
      250 = \frac{5}{2} W^2
      $$

3. **Solve for $$ W $$:**
    $$
    \frac{5}{2} W^2 = 250
    $$
    $$
    W^2 = 250 \times \frac{2}{5}
    $$
    $$
    W^2 = 100
    $$
    $$
    W = \sqrt{100}
    $$
    $$
    W = 10 \, \text{in}
    $$

4. **Verification:**
    - If $$ W = 10 \, \text{in} $$, then:
      $$
      L = \frac{5}{2} \times 10 = 25 \, \text{in}
      $$
    - Area:
      $$
      A = 25 \times 10 = 250 \, \text{in}^2
      $$
    - The values satisfy the given conditions.

**Answer:**  
**d. 10 in**
The width of the rectangle is 10 inches.

If a rectangle has a length that is equal to of its width) and the area is (2)
what is its width?
a. 625 in
b. 25 in
c. 100 in
d. 10 in
e. 125 in

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If a rectangle has a length that is equal to of its width) and the area is (2) what is its width? a. 625 in b. 25 in c. 100 in d. 10 in e. 125 in