The side of a square is \(x\) cm. If reducing the side by 9 cm makes the new area 1681 square cm, what was the original side of the square?
Answer and explanation
Correct answer: 50 cm
The reduced side is \((x-9)\) cm, so \((x-9)^2=1681=41^2\). Since a side length is positive and the reduced side must also be positive, \(x-9=41\), not \(-41\). Hence, \(x=50\) cm. Exam tip: In quadratic equations involving lengths, retain only the positive root that fits the situation.
Frequently asked questions
What is the correct answer to this question?
50 cm
Why is this the correct answer?
The reduced side is \((x-9)\) cm, so \((x-9)^2=1681=41^2\). Since a side length is positive and the reduced side must also be positive, \(x-9=41\), not \(-41\). Hence, \(x=50\) cm. Exam tip: In quadratic equations involving lengths, retain only the positive root that fits the situation.
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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