Question

solving a formula for a variable
solve for the width in the formula for the area of a rectangle.

use the rewritten formula to find the width of a rectangle with an area of 42 square inches and a length of 16.8 inches.

Explanation:

Part 1: Solve for the width in the area of a rectangle formula

Step1: Recall the area formula

The formula for the area \( A \) of a rectangle is \( A = l \times w \), where \( l \) is the length and \( w \) is the width.

Step2: Solve for \( w \)

To isolate \( w \), divide both sides of the equation by \( l \) (assuming \( l
eq 0 \)). So we get \( w=\frac{A}{l} \).

Step1: Identify given values

We know that the area \( A = 42 \) square inches and the length \( l = 16.5 \) inches. We use the formula \( w=\frac{A}{l} \) from part 1.

Step2: Substitute the values

Substitute \( A = 42 \) and \( l = 16.5 \) into the formula: \( w=\frac{42}{16.5} \).

Step3: Calculate the result

\( \frac{42}{16.5}=\frac{42\times2}{16.5\times2}=\frac{84}{33}=\frac{28}{11}\approx2.545 \) (rounded to three decimal places)

Answer:

\( w = \frac{A}{l} \)

Part 2: Find the width with given area and length