Question

a rectangular pan has a length that is \\(\frac{4}{3}\\) the width. the total area of the pan is \\(432\text{ in}^2\\). what is the width of the cake pan?
\\(a = lw\\)
\\(\bigcirc\\ 10.4\text{ in}\\)
\\(\bigcirc\\ 13.9\text{ in}\\)
\\(\bigcirc\\ 18\text{ in}\\)
\\(\bigcirc\\ 24\text{ in}\\)

Explanation:

Step1: Define variables

Let the width of the pan be \( w \). Then the length \( l = \frac{4}{3}w \).

Step2: Use area formula

The area of a rectangle is \( A = lw \). Substitute \( l = \frac{4}{3}w \) and \( A = 432 \) into the formula:

$$ 432=\frac{4}{3}w\times w $$

$$ 432=\frac{4}{3}w^{2} $$

Step3: Solve for \( w^{2} \)

Multiply both sides by \( \frac{3}{4} \):

$$ w^{2}=432\times\frac{3}{4} $$

$$ w^{2}=324 $$

Step4: Solve for \( w \)

Take the square root of both sides:

$$ w = \sqrt{324}= 18 $$

Answer:

18 in