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,
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Mathematics Problem: Solving for Poster Dimensions
Here are detailed steps and explanations for solving the given problem about the dimensions of a rectangular poster.
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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.*
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.
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Input Box
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**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 \( ax^2 + bx + c = 0 \), \( a = 1 \),](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe0f37d6-39ab-4894-bfb0-f755c5eb1ff1%2F22aafd15-dbb7-4e42-93fa-263783485c13%2Frzgx3vh_processed.jpeg&w=3840&q=75)
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