A rectangle has length \((x+8)\) and breadth \((x-5)\). If its area is \(104\) square units, which quadratic equation correctly represents this situation?
Answer and explanation
Correct answer: \(x^2+3x-144=0\)
Area of a rectangle = length × breadth, so \((x+8)(x-5)=104\). On expanding, we get \(x^2+3x-40=104\). Bringing all terms to one side gives \(x^2+3x-144=0\), so option A is correct. Option B results from failing to transfer the \(-40\) term correctly while simplifying. Exam tip: For area-based word problems, first write length × breadth = given area, then rearrange the equation into standard quadratic form.
Frequently asked questions
What is the correct answer to this question?
\(x^2+3x-144=0\)
Why is this the correct answer?
Area of a rectangle = length × breadth, so \((x+8)(x-5)=104\). On expanding, we get \(x^2+3x-40=104\). Bringing all terms to one side gives \(x^2+3x-144=0\), so option A is correct. Option B results from failing to transfer the \(-40\) term correctly while simplifying. Exam tip: For area-based word problems, first write length × breadth = given area, then rearrange the equation into standard quadratic form.
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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