The diagonal of a rectangle is 25 cm, and its length is 17 cm more than its breadth. What is the breadth of the rectangle?
Answer and explanation
Correct answer: 7 cm
Let the breadth of the rectangle be \(x\) cm. Then its length is \(x+17\) cm. By the Pythagorean theorem, \(x^2+(x+17)^2=25^2\). On simplifying, we get \(x^2+17x-168=0\), or \((x-7)(x+24)=0\). Thus, \(x=7\) or \(x=-24\). Since a length cannot be negative, the breadth is 7 cm. Exam tip: Treat the diagonal, length, and breadth as the sides of a right triangle and reject any negative root obtained from the quadratic equation.
Frequently asked questions
What is the correct answer to this question?
7 cm
Why is this the correct answer?
Let the breadth of the rectangle be \(x\) cm. Then its length is \(x+17\) cm. By the Pythagorean theorem, \(x^2+(x+17)^2=25^2\). On simplifying, we get \(x^2+17x-168=0\), or \((x-7)(x+24)=0\). Thus, \(x=7\) or \(x=-24\). Since a length cannot be negative, the breadth is 7 cm. Exam tip: Treat the diagonal, length, and breadth as the sides of a right triangle and reject any negative root obtained from 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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