A wire is bent into a square and the area is 3025 cm². What is the length of the wire?
Answer and explanation
Correct answer: 220 cm
Let the side of the square be s centimetres. The area formula for a square is s², so s² = 3025. Since a length is positive, s = √3025 = 55 cm, not −55 cm. The wire forms the complete boundary of the square, so its length equals the perimeter, 4s. Therefore the wire length is 4 × 55 = 220 cm, making option C correct. Option A and option B do not equal four times the side, while option D would correspond to an incorrect side length of 60 cm. The important modelling step is to distinguish area, which is measured in square centimetres, from the wire length, which is the perimeter measured in centimetres.
Frequently asked questions
What is the correct answer to this question?
220 cm
Why is this the correct answer?
Let the side of the square be s centimetres. The area formula for a square is s², so s² = 3025. Since a length is positive, s = √3025 = 55 cm, not −55 cm. The wire forms the complete boundary of the square, so its length equals the perimeter, 4s. Therefore the wire length is 4 × 55 = 220 cm, making option C correct. Option A and option B do not equal four times the side, while option D would correspond to an incorrect side length of 60 cm. The important modelling step is to distinguish area, which is measured in square centimetres, from the wire length, which is the perimeter measured in centimetres.
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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