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

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

Options:

Correct Answer: 8 cm

Solution:

Let the width be x. Then, length = 3x. The perimeter is 2(length + width) = 48. So, 2(3x + x) = 48. Simplifying gives 8x = 48, thus x = 6 cm.

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

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

Step 1: Let the width of the rectangle be represented by the variable x.
Step 2: Since the length is 3 times the width, we can express the length as 3x.
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(3x + x).
Step 5: Simplify the expression inside the parentheses: 3x + x = 4x, so we have P = 2(4x).
Step 6: Now, calculate the perimeter: 2(4x) = 8x.
Step 7: We know the perimeter is 48 cm, so set up the equation: 8x = 48.
Step 8: To find x, divide both sides of the equation by 8: x = 48 / 8.
Step 9: Calculate the value: x = 6 cm. This means the width of the rectangle is 6 cm.

Perimeter of a Rectangle – Understanding how to calculate the perimeter using the formula P = 2(length + width).
Algebraic Expressions – Setting up equations based on relationships between length and width.
Solving Linear Equations – Solving for a variable in a linear equation derived from the perimeter formula.