Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To solve for the width of the rectangular pan, let's proceed with a step-by-step approach.
1. Express the Relationship Between Length and Width:
We are told the length (L) of the pan is [tex]\(\frac{4}{3}\)[/tex] times the width (W).
[tex]\[ L = \frac{4}{3}W \][/tex]
2. Express the Area in Terms of Width:
The area (A) of a rectangle is given by length times width.
[tex]\[ A = L \times W \][/tex]
Substituting the expression for length ([tex]\(L = \frac{4}{3}W\)[/tex]):
[tex]\[ A = \left(\frac{4}{3}W\right) \times W \][/tex]
Simplifying the right-hand side:
[tex]\[ A = \frac{4}{3}W^2 \][/tex]
3. Substitute the Given Area:
We are given that the total area of the pan is [tex]\(432 \, \text{in}^2\)[/tex].
[tex]\[ 432 = \frac{4}{3}W^2 \][/tex]
4. Solve for the Width (W):
[tex]\[ 432 = \frac{4}{3}W^2 \][/tex]
To isolate [tex]\(W^2\)[/tex], multiply both sides by [tex]\(\frac{3}{4}\)[/tex]:
[tex]\[ 432 \times \frac{3}{4} = W^2 \][/tex]
[tex]\[ 324 = W^2 \][/tex]
To find [tex]\(W\)[/tex], take the square root of both sides:
[tex]\[ W = \sqrt{324} \][/tex]
[tex]\[ W = 18 \, \text{in} \][/tex]
The width of the cake pan is [tex]\( \boxed{18 \, \text{in}} \)[/tex].
1. Express the Relationship Between Length and Width:
We are told the length (L) of the pan is [tex]\(\frac{4}{3}\)[/tex] times the width (W).
[tex]\[ L = \frac{4}{3}W \][/tex]
2. Express the Area in Terms of Width:
The area (A) of a rectangle is given by length times width.
[tex]\[ A = L \times W \][/tex]
Substituting the expression for length ([tex]\(L = \frac{4}{3}W\)[/tex]):
[tex]\[ A = \left(\frac{4}{3}W\right) \times W \][/tex]
Simplifying the right-hand side:
[tex]\[ A = \frac{4}{3}W^2 \][/tex]
3. Substitute the Given Area:
We are given that the total area of the pan is [tex]\(432 \, \text{in}^2\)[/tex].
[tex]\[ 432 = \frac{4}{3}W^2 \][/tex]
4. Solve for the Width (W):
[tex]\[ 432 = \frac{4}{3}W^2 \][/tex]
To isolate [tex]\(W^2\)[/tex], multiply both sides by [tex]\(\frac{3}{4}\)[/tex]:
[tex]\[ 432 \times \frac{3}{4} = W^2 \][/tex]
[tex]\[ 324 = W^2 \][/tex]
To find [tex]\(W\)[/tex], take the square root of both sides:
[tex]\[ W = \sqrt{324} \][/tex]
[tex]\[ W = 18 \, \text{in} \][/tex]
The width of the cake pan is [tex]\( \boxed{18 \, \text{in}} \)[/tex].
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.