The width of a rectangle is V84 ft and the length is 512 ft. What is the area of the rectangle? Answer

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem Statement:**

The width of a rectangle is \(\sqrt[3]{8^2}\) ft, and the length is \(512^{\frac{2}{3}}\) ft. What is the area of the rectangle?

**Solution:**

To find the area of the rectangle, use the formula:

\[ \text{Area} = \text{Width} \times \text{Length} \]

**Step 1: Calculate the Width**

\[
\sqrt[3]{8^2} = \sqrt[3]{64} = 4 \text{ ft}
\]

**Step 2: Calculate the Length**

\[
512^{\frac{2}{3}} = (512^{\frac{1}{3}})^2 = 8^2 = 64 \text{ ft}
\]

**Step 3: Calculate the Area**

\[
\text{Area} = 4 \, \text{ft} \times 64 \, \text{ft} = 256 \, \text{ft}^2
\]

**Answer:**

The area of the rectangle is \(256 \, \text{ft}^2\).

**Diagram Explanation:**

The diagram shows a rectangle with sides labeled to represent the area in square feet (\( \text{ft}^2 \)).
Transcribed Image Text:**Problem Statement:** The width of a rectangle is \(\sqrt[3]{8^2}\) ft, and the length is \(512^{\frac{2}{3}}\) ft. What is the area of the rectangle? **Solution:** To find the area of the rectangle, use the formula: \[ \text{Area} = \text{Width} \times \text{Length} \] **Step 1: Calculate the Width** \[ \sqrt[3]{8^2} = \sqrt[3]{64} = 4 \text{ ft} \] **Step 2: Calculate the Length** \[ 512^{\frac{2}{3}} = (512^{\frac{1}{3}})^2 = 8^2 = 64 \text{ ft} \] **Step 3: Calculate the Area** \[ \text{Area} = 4 \, \text{ft} \times 64 \, \text{ft} = 256 \, \text{ft}^2 \] **Answer:** The area of the rectangle is \(256 \, \text{ft}^2\). **Diagram Explanation:** The diagram shows a rectangle with sides labeled to represent the area in square feet (\( \text{ft}^2 \)).
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