The area of a rectangle is \(180\) square units, and its length is \(3\) times its breadth. What is the breadth?
Answer and explanation
Correct answer: \(2\sqrt{15}\)
Let the breadth be \(x\) units. Then the length is \(3x\) units. Using the area formula, \(x\times 3x=180\), so \(3x^2=180\). Hence, \(x^2=60\), and since a breadth must be positive, \(x=\sqrt{60}=2\sqrt{15}\) units. Therefore, option A is correct. Exam tip: For dimensions such as length and breadth, select only the positive root of the quadratic equation. Option C, \(15\), does not satisfy the given area because \(3(15)^2\neq 180\).
Frequently asked questions
What is the correct answer to this question?
\(2\sqrt{15}\)
Why is this the correct answer?
Let the breadth be \(x\) units. Then the length is \(3x\) units. Using the area formula, \(x\times 3x=180\), so \(3x^2=180\). Hence, \(x^2=60\), and since a breadth must be positive, \(x=\sqrt{60}=2\sqrt{15}\) units. Therefore, option A is correct. Exam tip: For dimensions such as length and breadth, select only the positive root of the quadratic equation. Option C, \(15\), does not satisfy the given area because \(3(15)^2\neq 180\).
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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