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Answer :
To solve the given problem, we need to set up an equation based on the information about the rectangle.
1. Understanding the Problem:
- We are given that the length of a rectangle is 4 units less than 5 times its width.
- We are also given that the area of the rectangle is 197 square units.
2. Setting Up the Equation:
- Let [tex]\( w \)[/tex] be the width of the rectangle.
- Then, the length of the rectangle can be expressed as [tex]\( 5w - 4 \)[/tex].
3. Using the Formula for Area:
- The area [tex]\( A \)[/tex] of a rectangle is given by the formula:
[tex]\[
\text{Area} = \text{length} \times \text{width}
\][/tex]
- Substituting the known values, we get:
[tex]\[
(5w - 4) \times w = 197
\][/tex]
4. Simplifying the Equation:
- Distribute [tex]\( w \)[/tex] in the expression:
[tex]\[
5w^2 - 4w = 197
\][/tex]
5. Identifying the Correct Equation:
- The equation we derived to find the width [tex]\( w \)[/tex] is [tex]\( 5w^2 - 4w = 197 \)[/tex].
This matches option A from the given choices. So, the correct equation that can be used to find [tex]\( w \)[/tex], the width of the rectangle, is:
A. [tex]\( 5w^2 - 4w = 197 \)[/tex]
1. Understanding the Problem:
- We are given that the length of a rectangle is 4 units less than 5 times its width.
- We are also given that the area of the rectangle is 197 square units.
2. Setting Up the Equation:
- Let [tex]\( w \)[/tex] be the width of the rectangle.
- Then, the length of the rectangle can be expressed as [tex]\( 5w - 4 \)[/tex].
3. Using the Formula for Area:
- The area [tex]\( A \)[/tex] of a rectangle is given by the formula:
[tex]\[
\text{Area} = \text{length} \times \text{width}
\][/tex]
- Substituting the known values, we get:
[tex]\[
(5w - 4) \times w = 197
\][/tex]
4. Simplifying the Equation:
- Distribute [tex]\( w \)[/tex] in the expression:
[tex]\[
5w^2 - 4w = 197
\][/tex]
5. Identifying the Correct Equation:
- The equation we derived to find the width [tex]\( w \)[/tex] is [tex]\( 5w^2 - 4w = 197 \)[/tex].
This matches option A from the given choices. So, the correct equation that can be used to find [tex]\( w \)[/tex], the width of the rectangle, is:
A. [tex]\( 5w^2 - 4w = 197 \)[/tex]
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