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Chapter 4 · Question 6

A rectangular hall has area 300 m2300\text{ m}^2 and length one metre more than twice its breadth. Form the quadratic equation for its breadth.

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Answer

Direct Answer

Let breadth be xx m. Length is (2x+1)(2x+1) m. Area =x(2x+1)=300=x(2x+1)=300, so 2x2+x−300=02x^2+x-300=0.

Simple Explanation

Translate breadth and length into algebra, then use area =l×b=l\times b.

Exam-Ready Structure

Let breadth =x=x m. Then length =(2x+1)=(2x+1) m. Since area is 300 m2300\text{ m}^2, x(2x+1)=300x(2x+1)=300. Expanding gives 2x2+x=3002x^2+x=300, hence 2x2+x−300=02x^2+x-300=0.

Key Points

  • Let breadth be xx m.

Related Questions

Q1

Define a quadratic equation and identify aa, bb, and cc in 2x2+x−300=02x^2+x-300=0.

Q2

Solve x2−5x+6=0x^2-5x+6=0 by factorisation.

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