The numerical value of the area of a square is 45 more than the numerical value of its perimeter. What is the side length of the square?
Answer and explanation
Correct answer: 9
Let the side of the square be \(x\). Its area is \(x^2\) and its perimeter is \(4x\). Therefore, \(x^2=4x+45\), giving \(x^2-4x-45=0\). Factoring, \((x-9)(x+5)=0\), so \(x=9\) or \(x=-5\). Since a length cannot be negative, the valid answer is 9. Exam tip: For a geometrical length, reject any negative root of the quadratic equation.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
Let the side of the square be \(x\). Its area is \(x^2\) and its perimeter is \(4x\). Therefore, \(x^2=4x+45\), giving \(x^2-4x-45=0\). Factoring, \((x-9)(x+5)=0\), so \(x=9\) or \(x=-5\). Since a length cannot be negative, the valid answer is 9. Exam tip: For a geometrical length, reject any negative root of the quadratic equation.
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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