Math Problem and Detailed Solution
Problem:
A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 64 meters,
find the dimensions of the rectangle.
Solution:
1. Understand the Problem:
• You know that the perimeter of a rectangle is calculated as:
\text{Perimeter} = 2 \times (\text{Length} + \text{Width})
• You also know that the length is 3 times the width:
\text{Length} = 3 \times \text{Width}
2. Set Up the Equations:
• Let W be the width of the rectangle.
• Then the length L can be expressed as:
L = 3W
• Substitute L = 3W into the perimeter formula:
64 = 2 \times (3W + W)
3. Simplify and Solve:
• Combine like terms inside the parentheses:
64 = 2 \times (4W)
• Simplify further:
64 = 8W
• Divide both sides by 8 to solve for W:
W = \frac{64}{8} = 8 \, \text{meters}
4. Find the Length:
• Now that you know the width W = 8 meters, substitute it back into the equation
for length:
Problem:
A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 64 meters,
find the dimensions of the rectangle.
Solution:
1. Understand the Problem:
• You know that the perimeter of a rectangle is calculated as:
\text{Perimeter} = 2 \times (\text{Length} + \text{Width})
• You also know that the length is 3 times the width:
\text{Length} = 3 \times \text{Width}
2. Set Up the Equations:
• Let W be the width of the rectangle.
• Then the length L can be expressed as:
L = 3W
• Substitute L = 3W into the perimeter formula:
64 = 2 \times (3W + W)
3. Simplify and Solve:
• Combine like terms inside the parentheses:
64 = 2 \times (4W)
• Simplify further:
64 = 8W
• Divide both sides by 8 to solve for W:
W = \frac{64}{8} = 8 \, \text{meters}
4. Find the Length:
• Now that you know the width W = 8 meters, substitute it back into the equation
for length:
