The length of a rectangle is 15 m more than its breadth. If the length is increased by 6 m and the breadth by 5 m, the new area becomes 1944 square metres. What is the approximate original breadth of the rectangle?
Answer and explanation
Correct answer: 31.81 m
Let the original breadth be x m. Then the original length is x+15 m. After the increases, the length is x+21 m and the breadth is x+5 m, so \((x+21)(x+5)=1944\). On simplifying, \(x^2+26x-1839=0\), whose positive solution is \(x=-13+2\sqrt{502}\approx31.81\). The negative solution is not valid for a length or breadth. Exam tip: In dimension-change problems, define one dimension as x and equate the product of the changed dimensions to the new area.
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What is the correct answer to this question?
31.81 m
Why is this the correct answer?
Let the original breadth be x m. Then the original length is x+15 m. After the increases, the length is x+21 m and the breadth is x+5 m, so \((x+21)(x+5)=1944\). On simplifying, \(x^2+26x-1839=0\), whose positive solution is \(x=-13+2\sqrt{502}\approx31.81\). The negative solution is not valid for a length or breadth. Exam tip: In dimension-change problems, define one dimension as x and equate the product of the changed dimensions to the new area.
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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