The diagonal of a rectangle is 25 units, and its length is 17 units more than its breadth. What is the breadth of the rectangle?
Answer and explanation
Correct answer: 7
Let the breadth be \(x\) units. Then the length is \(x+17\) units. By the Pythagorean theorem, \(x^2+(x+17)^2=25^2\), which simplifies to \(x^2+17x-168=0\). Factoring gives \((x-7)(x+24)=0\), so \(x=7\) or \(x=-24\). Since a breadth cannot be negative, the valid answer is 7. Exam tip: For rectangle problems involving the length, breadth, and diagonal, apply the Pythagorean theorem first.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
Let the breadth be \(x\) units. Then the length is \(x+17\) units. By the Pythagorean theorem, \(x^2+(x+17)^2=25^2\), which simplifies to \(x^2+17x-168=0\). Factoring gives \((x-7)(x+24)=0\), so \(x=7\) or \(x=-24\). Since a breadth cannot be negative, the valid answer is 7. Exam tip: For rectangle problems involving the length, breadth, and diagonal, apply the Pythagorean theorem first.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
