A square park has the same area as a rectangular park. The side of the square is 42 m, while the rectangle has breadth \(x\) m and length \((x+20)\) m. What is the exact value of the rectangle’s breadth \(x\)?
Answer and explanation
Correct answer: \(-10+2\sqrt{466}\)
Since the areas are equal, \(x(x+20)=42^2=1764\). Therefore, \(x^2+20x-1764=0\). Using the quadratic formula, \(x=\frac{-20\pm\sqrt{20^2+4(1764)}}{2}=-10\pm2\sqrt{466}\). Because a breadth must be positive, the valid value is \(x=-10+2\sqrt{466}\approx33.17\) m; the negative root is not physically meaningful. In such problems, first form the area equation and then reject any root that makes a length negative.
Frequently asked questions
What is the correct answer to this question?
\(-10+2\sqrt{466}\)
Why is this the correct answer?
Since the areas are equal, \(x(x+20)=42^2=1764\). Therefore, \(x^2+20x-1764=0\). Using the quadratic formula, \(x=\frac{-20\pm\sqrt{20^2+4(1764)}}{2}=-10\pm2\sqrt{466}\). Because a breadth must be positive, the valid value is \(x=-10+2\sqrt{466}\approx33.17\) m; the negative root is not physically meaningful. In such problems, first form the area equation and then reject any root that makes a length negative.
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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