Questions: Model with Math What is the width of the rectangle written as an exponential expression?

Solution Steps

The problem provides the area of the rectangle as \(10^4 \, \text{m}^2\) and the length of the rectangle as \(10^3 \, \text{m}\).

The area \(A\) of a rectangle is given by the formula: \[ A = \text{length} \times \text{width} \] Here, \(A = 10^4 \, \text{m}^2\) and the length \(L = 10^3 \, \text{m}\).

Rearrange the area formula to solve for the width \(W\): \[ W = \frac{A}{L} \] Substitute the given values: \[ W = \frac{10^4 \, \text{m}^2}{10^3 \, \text{m}} \]

Simplify the division of the exponential expressions: \[ W = 10^{4-3} \, \text{m} \] \[ W = 10^1 \, \text{m} \] \[ W = 10 \, \text{m} \]

Final Answer