The length of a rectangle is \\(2x+1\\) units and its breadth is \\(x-4\\) units. If its area is \\(45\\) square units, which quadratic equation represents this situation?
Answer and explanation
Correct answer: \\(2x^2-7x-49=0\\)
The area of a rectangle is length × breadth, so \\((2x+1)(x-4)=45\\). Expanding the product gives \\(2x^2-8x+x-4=2x^2-7x-4\\). Therefore, \\(2x^2-7x-4=45\\), which simplifies to \\(2x^2-7x-49=0\\). Hence, option A is correct. Exam tip: For area-based questions, first form the product equation and then bring all terms to one side to make it equal to zero.
Frequently asked questions
What is the correct answer to this question?
\\(2x^2-7x-49=0\\)
Why is this the correct answer?
The area of a rectangle is length × breadth, so \\((2x+1)(x-4)=45\\). Expanding the product gives \\(2x^2-8x+x-4=2x^2-7x-4\\). Therefore, \\(2x^2-7x-4=45\\), which simplifies to \\(2x^2-7x-49=0\\). Hence, option A is correct. Exam tip: For area-based questions, first form the product equation and then bring all terms to one side to make it equal to zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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