WAEC 2010 Mathematics · Question 11
A rectangle has length xcm and width (x - 1)cm. If the perimeter is 16cm. Find the value of x
Options
- A.3cm
- B.4cm
- C.4cm
- D.5cm
Answer: C. 4cm
Explanation written with AI and checked against the answer key
Analyze the question: We have a rectangle with length x cm and width (x − 1) cm. Its perimeter is 16 cm, and we need x. Concept: The perimeter of a rectangle is P = 2(length + width) Solution: 2[x + (x − 1)] = 16 2(2x − 1) = 16 4x − 2 = 16 4x = 18 x = 18/4 = 4½ cm Check: Length = 4.5 cm, width = 3.5 cm. Perimeter = 2(4.5 + 3.5) = 2(8) = 16 cm ✓ Tip: Always substitute your answer back into the perimeter formula to confirm it. Also remember that perimeter uses 2(l + w), and forgetting the "2" is a common mistake. If you had forgotten it, you would have got x = 4.5 only by luck in the wrong equation, so write each step carefully. (Here, without the 2, you'd get 2x − 1 = 16, giving 8.5, which is not an option, a sign something went wrong.)AI can make mistakes. Report anything that looks wrong.
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