The side length of a square is \(x\) cm. If the side length is reduced by 5 cm, the area of the resulting square becomes 784 square cm. What was the original side length of the square?
Answer and explanation
Correct answer: 33 cm
The reduced side is \((x-5)\) cm, so \((x-5)^2=784=28^2\). Since a side length must be positive, take \(x-5=28\), giving \(x=33\) cm. The other algebraic possibility, \(x-5=-28\), gives \(x=-23\) cm, which is not physically meaningful. Exam tip: After finding the reduced side from the area, add back the length that was removed.
Frequently asked questions
What is the correct answer to this question?
33 cm
Why is this the correct answer?
The reduced side is \((x-5)\) cm, so \((x-5)^2=784=28^2\). Since a side length must be positive, take \(x-5=28\), giving \(x=33\) cm. The other algebraic possibility, \(x-5=-28\), gives \(x=-23\) cm, which is not physically meaningful. Exam tip: After finding the reduced side from the area, add back the length that was removed.
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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