The perimeter of a rectangle is 160 cm. It is given that the rectangle is four times as long as it is wide. Using this information, determine the exact length and width of the rectangle in centimetres.

Introduction / Context: This question tests basic understanding of rectangle geometry and perimeter relations. When a rectangle’s perimeter and the ratio between its length and width are known, the actual dimensions can be found by forming a simple algebraic equation.

Given Data / Assumptions:

• Perimeter = 160 cm
• Length is four times the width
• Let width = b cm
• Then length = 4b cm

Concept / Approach: The perimeter of a rectangle is given by 2*(length + breadth). Substitute the given relationship between length and width into the perimeter formula and solve for the unknown dimension.

Step-by-Step Solution: Perimeter = 2*(l + b) 160 = 2*(4b + b) 160 = 2*5b = 10b b = 16 cm l = 4b = 4*16 = 64 cm

Verification / Alternative check: Substituting l = 64 and b = 16 into the perimeter formula gives 2*(64 + 16) = 2*80 = 160 cm, which matches the given perimeter exactly.

Why Other Options Are Wrong: 48 cm and 24 cm: length is only twice the width, not four times. 65 cm and 16 cm: perimeter exceeds 160 cm. 16 cm and 64 cm: reverses length and width. 40 cm and 20 cm: does not satisfy the four-times condition.

Common Pitfalls: Forgetting to multiply the sum by 2 in the perimeter formula. Mixing up which dimension is four times the other. Arithmetic errors while solving for b.

Final Answer: Length = 64 cm and Width = 16 cm