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Part A The width of an extra large rectangular poster is 8 inches more than half its length. The area of this poster is 306 square inches. Write an equation in one variable that could be used to find the number of inches in the dimensions of this poster. In the box below, clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for the question to determine your answer. Click the box below to type your math work and answer. On the right side of the box, click the - button to start a new line. ) Part B Solve this equation algebraically to determine the dimensions of this poster, in inches. In the box below, clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for the question to determine your answer,

Part A The width of an extra large rectangular poster is 8 inches more than half its length. The area of this poster is 306 square inches. Write an equation in one variable that could be used to find the number of inches in the dimensions of this poster. In the box below, clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for the question to determine your answer. Click the box below to type your math work and answer. On the right side of the box, click the - button to start a new line. ) Part B Solve this equation algebraically to determine the dimensions of this poster, in inches. In the box below, clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for the question to determine your answer,

Algebra and Trigonometry (6th Edition)
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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### Mathematics Problem: Solving for Poster Dimensions Here are detailed steps and explanations for solving the given problem about the dimensions of a rectangular poster. --- **Part A** *The width of an extra large rectangular poster is 8 inches more than half its length. The area of this poster is 306 square inches. Write an equation in one variable that could be used to find the number of inches in the dimensions of this poster.* 1. **Define the variables:** - Let \( L \) represent the length of the poster in inches. - The width \( W \) can be expressed as 8 inches more than half its length, i.e., \( W = \frac{L}{2} + 8 \). 2. **Express the area relation:** - The area \( A \) of a rectangle is given by the formula \( A = L \times W \). - Here, \( A = 306 \) square inches. 3. **Substitute the width expression into the area equation:** - \( 306 = L \times \left( \frac{L}{2} + 8 \right) \). 4. **Form the equation:** - \( 306 = \frac{L^2}{2} + 8L \). 5. **Simplify to get a standard form equation:** - Multiply through by 2 to clear the fraction: \( 612 = L^2 + 16L \). - Rearrange to form a standard quadratic equation: \( L^2 + 16L - 612 = 0 \). **On the right side of the box, click the "+" button to start a new line.** Click the box below to type your math work and answer. ``` Input Box ``` --- **Part B** *Solve this equation algebraically to determine the dimensions of this poster, in inches.* 1. **Restate the quadratic equation from Part A:** - \( L^2 + 16L - 612 = 0 \). 2. **Solve the quadratic equation using factoring, completing the square, or quadratic formula. Here we'll use the quadratic formula \( L = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \):** - For equation \( ax^2 + bx + c = 0 \), \( a = 1 \),
Transcribed Image Text:### Mathematics Problem: Solving for Poster Dimensions Here are detailed steps and explanations for solving the given problem about the dimensions of a rectangular poster. --- **Part A** *The width of an extra large rectangular poster is 8 inches more than half its length. The area of this poster is 306 square inches. Write an equation in one variable that could be used to find the number of inches in the dimensions of this poster.* 1. **Define the variables:** - Let \( L \) represent the length of the poster in inches. - The width \( W \) can be expressed as 8 inches more than half its length, i.e., \( W = \frac{L}{2} + 8 \). 2. **Express the area relation:** - The area \( A \) of a rectangle is given by the formula \( A = L \times W \). - Here, \( A = 306 \) square inches. 3. **Substitute the width expression into the area equation:** - \( 306 = L \times \left( \frac{L}{2} + 8 \right) \). 4. **Form the equation:** - \( 306 = \frac{L^2}{2} + 8L \). 5. **Simplify to get a standard form equation:** - Multiply through by 2 to clear the fraction: \( 612 = L^2 + 16L \). - Rearrange to form a standard quadratic equation: \( L^2 + 16L - 612 = 0 \). **On the right side of the box, click the "+" button to start a new line.** Click the box below to type your math work and answer. ``` Input Box ``` --- **Part B** *Solve this equation algebraically to determine the dimensions of this poster, in inches.* 1. **Restate the quadratic equation from Part A:** - \( L^2 + 16L - 612 = 0 \). 2. **Solve the quadratic equation using factoring, completing the square, or quadratic formula. Here we'll use the quadratic formula \( L = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \):** - For equation \( ax^2 + bx + c = 0 \), \( a = 1 \),
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