The side length of a square is \(x\) cm. If reducing the side by 7 cm makes the new area 1296 square cm, what was the original side length?
Answer and explanation
Correct answer: 43 cm
After the reduction, the side of the square is \(x-7\) cm. Thus, \((x-7)^2=1296=36^2\). Since a side length is positive, \(x-7=36\), giving \(x=43\) cm. The other algebraic root, \(x-7=-36\), gives \(x=-29\) cm, which is not a valid side length. Exam tip: find the reduced side from the area first, then add back the amount reduced.
Frequently asked questions
What is the correct answer to this question?
43 cm
Why is this the correct answer?
After the reduction, the side of the square is \(x-7\) cm. Thus, \((x-7)^2=1296=36^2\). Since a side length is positive, \(x-7=36\), giving \(x=43\) cm. The other algebraic root, \(x-7=-36\), gives \(x=-29\) cm, which is not a valid side length. Exam tip: find the reduced side from the area first, then add back the amount reduced.
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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