The area of a rectangle is 2170 square centimetres, and its length is 27 centimetres more than its breadth. What is the perimeter of the rectangle?
Answer and explanation
Correct answer: 194 cm
Let the breadth be \(x\) cm. Then the length is \(x+27\) cm, so \(x(x+27)=2170\), or \(x^2+27x-2170=0\). The positive solution is \(x=35\), giving breadth 35 cm and length 62 cm. Hence, the perimeter is \(2(35+62)=194\) cm. Exam tip: In rectangle word problems, form the quadratic equation from the area and retain only the positive dimension.
Frequently asked questions
What is the correct answer to this question?
194 cm
Why is this the correct answer?
Let the breadth be \(x\) cm. Then the length is \(x+27\) cm, so \(x(x+27)=2170\), or \(x^2+27x-2170=0\). The positive solution is \(x=35\), giving breadth 35 cm and length 62 cm. Hence, the perimeter is \(2(35+62)=194\) cm. Exam tip: In rectangle word problems, form the quadratic equation from the area and retain only the positive dimension.
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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