A rectangle's length is three times its width. If the perimeter is 64 cm, what i

A rectangle's length is three times its width. If the perimeter is 64 cm, what is the area of the rectangle?

A rectangle's length is three times its width. If the perimeter is 64 cm, what is the area of the rectangle?

Step 1: Let the width of the rectangle be represented as 'x'.
Step 2: Since the length is three times the width, we can express the length as '3x'.
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(3x + x)'.
Step 5: Simplify the expression inside the parentheses: '3x + x = 4x', so the perimeter becomes 'Perimeter = 2(4x)'.
Step 6: This simplifies to 'Perimeter = 8x'.
Step 7: We know the perimeter is 64 cm, so set up the equation: '8x = 64'.
Step 8: Solve for 'x' by dividing both sides of the equation by 8: 'x = 64 / 8'.
Step 9: Calculate 'x', which gives 'x = 8 cm'. This is the width of the rectangle.
Step 10: Now, find the length by substituting 'x' back into the length expression: 'length = 3x = 3(8)'.
Step 11: Calculate the length: 'length = 24 cm'.
Step 12: Now, calculate the area of the rectangle using the formula 'Area = length × width'.
Step 13: Substitute the values for length and width: 'Area = 24 × 8'.
Step 14: Calculate the area: 'Area = 192 cm²'.

Perimeter of a Rectangle – Understanding how to calculate the perimeter using the formula P = 2(length + width).
Area of a Rectangle – Calculating the area using the formula A = length × width.
Algebraic Representation – Using variables to represent dimensions and solving equations.