A wire is bent into a square and the area is 1296 square cm. What is the length of the wire?
Answer and explanation
Correct answer: 144 cm
When a wire is bent into a square, the wire length becomes the perimeter of the square. Let the side be s cm. The area condition gives s² = 1296, so s = 36 because a length must be positive. The perimeter, and hence the length of the wire, is 4s = 4×36 = 144 cm. Therefore option C is correct. Option A could result from an incorrect side length of 30 cm, while options B and D do not equal four times the valid side. The negative square-root value −36 is rejected because geometric length cannot be negative. A direct check also confirms that a square of side 36 cm has area 36² = 1296 square cm and perimeter 144 cm.
Frequently asked questions
What is the correct answer to this question?
144 cm
Why is this the correct answer?
When a wire is bent into a square, the wire length becomes the perimeter of the square. Let the side be s cm. The area condition gives s² = 1296, so s = 36 because a length must be positive. The perimeter, and hence the length of the wire, is 4s = 4×36 = 144 cm. Therefore option C is correct. Option A could result from an incorrect side length of 30 cm, while options B and D do not equal four times the valid side. The negative square-root value −36 is rejected because geometric length cannot be negative. A direct check also confirms that a square of side 36 cm has area 36² = 1296 square cm and perimeter 144 cm.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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