A rectangle's length is 3 times its width. If the perimeter is 48, what is the w

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Question: A rectangle\'s length is 3 times its width. If the perimeter is 48, what is the width?

Options:

Correct Answer: 6

Solution:

Let the width be w. Then the length is 3w. The perimeter is 2(w + 3w) = 48. Simplifying gives 8w = 48. Dividing by 8 gives w = 6.

A rectangle's length is 3 times its width. If the perimeter is 48, what is the width?

A rectangle's length is 3 times its width. If the perimeter is 48, what is the width?

Step 1: Let the width of the rectangle be represented by the variable 'w'.
Step 2: Since the length is 3 times the width, we can express the length as '3w'.
Step 3: The formula for the perimeter of a rectangle is P = 2(length + width).
Step 4: Substitute the expressions for length and width into the perimeter formula: P = 2(3w + w).
Step 5: Simplify the expression inside the parentheses: 3w + w = 4w, so the perimeter becomes P = 2(4w).
Step 6: Now, calculate the perimeter: P = 8w.
Step 7: We know the perimeter is 48, so set up the equation: 8w = 48.
Step 8: To find 'w', divide both sides of the equation by 8: w = 48 / 8.
Step 9: Calculate the result: w = 6.

Perimeter of a Rectangle – Understanding how to calculate the perimeter using the formula P = 2(length + width).
Algebraic Expressions – Setting up and solving equations based on relationships between variables.
Proportional Relationships – Recognizing and applying the relationship between length and width in a rectangle.