The perimeter of a rectangle is 46 cm and its area is 126 cm². What is the length of its larger side?
Answer and explanation
Correct answer: 14 सेमी
Let the sides of the rectangle be \(x\) cm and \(y\) cm. From the perimeter, \(2(x+y)=46\), so \(x+y=23\). The area gives \(xy=126\). Therefore, \(x(23-x)=126\), which becomes \(x^2-23x+126=0\), or \((x-9)(x-14)=0\). Thus, the sides are 9 cm and 14 cm, so the larger side is 14 cm. Exam tip: divide the perimeter by 2 first to obtain the sum of the two sides.
Frequently asked questions
What is the correct answer to this question?
14 सेमी
Why is this the correct answer?
Let the sides of the rectangle be \(x\) cm and \(y\) cm. From the perimeter, \(2(x+y)=46\), so \(x+y=23\). The area gives \(xy=126\). Therefore, \(x(23-x)=126\), which becomes \(x^2-23x+126=0\), or \((x-9)(x-14)=0\). Thus, the sides are 9 cm and 14 cm, so the larger side is 14 cm. Exam tip: divide the perimeter by 2 first to obtain 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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