If a rectangle has a length that is twice its width and the perimeter is 48 cm,

If a rectangle has a length that is twice its width and the perimeter is 48 cm, what is the area of the rectangle?

If a rectangle has a length that is twice its width and the perimeter is 48 cm, what is the area of the rectangle?

Step 1: Let the width of the rectangle be represented as 'w'.
Step 2: Since the length is twice the width, we can express the length as '2w'.
Step 3: The formula for the perimeter of a rectangle is Perimeter = 2(length + width).
Step 4: Substitute the expressions for length and width into the perimeter formula: Perimeter = 2(2w + w).
Step 5: We know the perimeter is 48 cm, so set up the equation: 2(2w + w) = 48.
Step 6: Simplify the equation: 2(3w) = 48, which gives us 6w = 48.
Step 7: Solve for 'w' by dividing both sides by 6: w = 48 / 6, so w = 8 cm.
Step 8: Now, find the length by substituting 'w' back into the length equation: length = 2w = 2 * 8 = 16 cm.
Step 9: Calculate the area of the rectangle using the formula Area = length * width: Area = 16 * 8.
Step 10: Finally, calculate the area: Area = 128 cm².

Perimeter of a Rectangle – Understanding how to calculate the perimeter using the formula P = 2(length + width).
Area of a Rectangle – Knowing how to calculate the area using the formula A = length * width.
Algebraic Manipulation – Ability to set up and solve equations based on given relationships between dimensions.