The diagonal of a rectangle is 13 units long, and its length is 7 units more than its breadth. What is the breadth of the rectangle?
Answer and explanation
Correct answer: 5
Let the breadth be \(x\) units; then the length is \(x+7\) units. By the Pythagorean theorem, \(x^2+(x+7)^2=13^2\). On simplifying, \(x^2+7x-60=0\), or \((x+12)(x-5)=0\). Thus \(x=5\) or \(x=-12\). Since a breadth cannot be negative, the breadth is 5 units. Option 12 is a distractor related to the negative root \(-12\). Exam tip: Reject negative values when a variable represents a physical length or distance.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Let the breadth be \(x\) units; then the length is \(x+7\) units. By the Pythagorean theorem, \(x^2+(x+7)^2=13^2\). On simplifying, \(x^2+7x-60=0\), or \((x+12)(x-5)=0\). Thus \(x=5\) or \(x=-12\). Since a breadth cannot be negative, the breadth is 5 units. Option 12 is a distractor related to the negative root \(-12\). Exam tip: Reject negative values when a variable represents a physical length or distance.
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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