A rectangular plot has a perimeter of 60 metres and an area of 216 square metres. What is the length of its longer side?
Answer and explanation
Correct answer: 18
The sum of the two sides of a rectangle is half its perimeter, so the sum is \(60/2=30\) metres. If one side is \(x\) metres, the other is \(30-x\) metres. Thus, \(x(30-x)=216\), giving \(x^2-30x+216=0\). Factoring gives \((x-18)(x-12)=0\), so the sides are 18 metres and 12 metres. Therefore, the longer side is 18 metres. In exams, first use half the perimeter to find the sum of the two sides.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The sum of the two sides of a rectangle is half its perimeter, so the sum is \(60/2=30\) metres. If one side is \(x\) metres, the other is \(30-x\) metres. Thus, \(x(30-x)=216\), giving \(x^2-30x+216=0\). Factoring gives \((x-18)(x-12)=0\), so the sides are 18 metres and 12 metres. Therefore, the longer side is 18 metres. In exams, first use half the perimeter to find the sum of the two sides.
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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