If a rectangle has a length that is equal to \( \frac{5}{2} \) of its width and the area is \( 250 \mathrm{in}^{2} \) what is its width?

To find the width of the rectangle, we can let the width be represented as \( w \). According to the information provided, the length can be expressed as \( l = \frac{5}{2}w \). Next, we can use the formula for the area of a rectangle, which is: \[ \text{Area} = \text{length} \times \text{width} \] Substituting the known values into this formula gives us: \[ 250 = \left(\frac{5}{2}w\right) \times w \] Multiplying this out results in: \[ 250 = \frac{5}{2}w^2 \] To eliminate the fraction, we can multiply both sides by 2: \[ 500 = 5w^2 \] Now, we can divide both sides by 5: \[ 100 = w^2 \] Taking the square root of both sides gives us: \[ w = 10 \] Hence, the width of the rectangle is \( 10 \, \text{inches} \).