A rectangle has an area of 888 square cm, and its length is 13 cm more than its breadth. What is the perimeter of the rectangle?
Answer and explanation
Correct answer: 122 cm
Let the breadth be \(x\) cm. Then the length is \(x+13\) cm. Using the area, \(x(x+13)=888\), so \(x^2+13x-888=0\). Factoring gives \((x-24)(x+37)=0\). The positive root gives a breadth of 24 cm and a length of 37 cm. Hence, the perimeter is \(2(24+37)=122\) cm. The negative root \(-37\) cannot represent a side length. Exam tip: In rectangle word problems, assign \(x\) to one side and express the other side using the stated difference before forming the quadratic equation.
Frequently asked questions
What is the correct answer to this question?
122 cm
Why is this the correct answer?
Let the breadth be \(x\) cm. Then the length is \(x+13\) cm. Using the area, \(x(x+13)=888\), so \(x^2+13x-888=0\). Factoring gives \((x-24)(x+37)=0\). The positive root gives a breadth of 24 cm and a length of 37 cm. Hence, the perimeter is \(2(24+37)=122\) cm. The negative root \(-37\) cannot represent a side length. Exam tip: In rectangle word problems, assign \(x\) to one side and express the other side using the stated difference before forming 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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