The diagonal of a rectangle is 25 cm, and its length is 5 cm greater than its breadth. What is the breadth of the rectangle?
Answer and explanation
Correct answer: 15 cm
Let the breadth of the rectangle be \(x\) cm. Its length is then \(x+5\) cm. By the Pythagorean theorem, \(x^2+(x+5)^2=25^2\), which simplifies to \(x^2+5x-300=0\). Factoring gives \((x+20)(x-15)=0\), so \(x=15\) or \(x=-20\). Since a length cannot be negative, the breadth is 15 cm. Exam tip: identify the length, breadth and diagonal as the sides of a right triangle before applying the Pythagorean theorem.
Frequently asked questions
What is the correct answer to this question?
15 cm
Why is this the correct answer?
Let the breadth of the rectangle be \(x\) cm. Its length is then \(x+5\) cm. By the Pythagorean theorem, \(x^2+(x+5)^2=25^2\), which simplifies to \(x^2+5x-300=0\). Factoring gives \((x+20)(x-15)=0\), so \(x=15\) or \(x=-20\). Since a length cannot be negative, the breadth is 15 cm. Exam tip: identify the length, breadth and diagonal as the sides of a right triangle before applying the Pythagorean theorem.
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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