The numerical value of the area of a square is 96 more than the numerical value of its perimeter. What is the side length of the square?
Answer and explanation
Correct answer: 12
Let the side of the square be x. Its area is x² and its perimeter is 4x. According to the question, x² = 4x + 96, so x² − 4x − 96 = 0. Factoring gives (x − 12)(x + 8) = 0. Thus x = 12 or −8; a side length cannot be negative, so the correct answer is 12. Exam tip: In measurement problems, retain only the positive root.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Let the side of the square be x. Its area is x² and its perimeter is 4x. According to the question, x² = 4x + 96, so x² − 4x − 96 = 0. Factoring gives (x − 12)(x + 8) = 0. Thus x = 12 or −8; a side length cannot be negative, so the correct answer is 12. Exam tip: In measurement problems, retain only the positive root.
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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