A square has side length \(x\) cm. If its side is reduced by 3 cm, its area becomes 225 square cm. What was the original side length?
Answer and explanation
Correct answer: 18 cm
The reduced side is \((x-3)\) cm, so \((x-3)^2=225\). This gives \(x-3=\pm15\). Since a side length must be positive and the reduced side is 15 cm, \(x-3=15\), hence \(x=18\) cm. The negative possibility would give \(x=-12\) cm, which is not physically valid. Exam tip: reject any root that gives a negative length in a geometric word problem.
Frequently asked questions
What is the correct answer to this question?
18 cm
Why is this the correct answer?
The reduced side is \((x-3)\) cm, so \((x-3)^2=225\). This gives \(x-3=\pm15\). Since a side length must be positive and the reduced side is 15 cm, \(x-3=15\), hence \(x=18\) cm. The negative possibility would give \(x=-12\) cm, which is not physically valid. Exam tip: reject any root that gives a negative length in a geometric word problem.
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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