A rectangle has a length that is twice its width. If the perimeter of the rectan

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

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

Step 1: Let the width of the rectangle be x cm.
Step 2: Since the length is twice the width, the length is 2x cm.
Step 3: The formula for the perimeter of a rectangle is 2(length + width).
Step 4: Substitute the values for length and width into the perimeter formula: 2(2x + x) = 48.
Step 5: Simplify the equation: 2(3x) = 48.
Step 6: Divide both sides by 2: 3x = 24.
Step 7: Divide both sides by 3 to find x: x = 8 cm (this is the width).
Step 8: Now, find the length by substituting x back: length = 2x = 2(8) = 16 cm.
Step 9: Calculate the area using the formula: Area = length × width = 16 cm × 8 cm.
Step 10: Multiply to find the area: Area = 128 cm².

Perimeter and Area of a Rectangle – Understanding the relationship between the length, width, perimeter, and area of a rectangle.
Algebraic Manipulation – Using algebra to solve for unknown variables based on given relationships.