The area of a rectangle is \(216\) square units, and its length is \(6\) units more than its breadth. What is the breadth of the rectangle?
Answer and explanation
Correct answer: 12
Let the breadth be \(x\) units. Then the length is \(x+6\) units. Using the area, \(x(x+6)=216\), so \(x^2+6x-216=0\). Factoring gives \((x-12)(x+18)=0\), leading to \(x=12\) or \(x=-18\). Since a length cannot be negative, the breadth is \(12\) units. Exam tip: In rectangle word problems, assign \(x\) to the smaller dimension and form the area equation first.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Let the breadth be \(x\) units. Then the length is \(x+6\) units. Using the area, \(x(x+6)=216\), so \(x^2+6x-216=0\). Factoring gives \((x-12)(x+18)=0\), leading to \(x=12\) or \(x=-18\). Since a length cannot be negative, the breadth is \(12\) units. Exam tip: In rectangle word problems, assign \(x\) to the smaller dimension and form the area equation first.
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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