A rectangle has length \((x+10)\) and breadth \((x-7)\). If its area is \(160\), which equation is correct?
Answer and explanation
Correct answer: \(x^2+3x-230=0\)
Area gives \((x+10)(x-7)=160\). Expanding the left side yields \(x^2+3x-70=160\). Bringing 160 to the left gives \(x^2+3x-70-160=0\), i.e. \(x^2+3x-230=0\), so option A is correct. The closest wrong option is B, which has the constant term \(-160\) instead of \(-230\) — a typical mistake from not moving the right-hand term across correctly. Exam tip: first expand, then move all terms to one side to form the quadratic and carefully check signs and arithmetic.
Frequently asked questions
What is the correct answer to this question?
\(x^2+3x-230=0\)
Why is this the correct answer?
Area gives \((x+10)(x-7)=160\). Expanding the left side yields \(x^2+3x-70=160\). Bringing 160 to the left gives \(x^2+3x-70-160=0\), i.e. \(x^2+3x-230=0\), so option A is correct. The closest wrong option is B, which has the constant term \(-160\) instead of \(-230\) — a typical mistake from not moving the right-hand term across correctly. Exam tip: first expand, then move all terms to one side to form the quadratic and carefully check signs and arithmetic.
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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