A square garden has area (169) square m. What is its side?
Answer and explanation
Correct answer: (13) m
The area of a square is obtained by multiplying its side by itself. If the side length is x metres, the area is \\(x^2\\) square metres. The given area is 169 square metres, so the equation is \\(x^2=169\\). We need the length whose square is 169. Since \\(13\times13=169\\), the positive length is 13 metres.
Although the algebraic equation has the solutions \\(x=13\\) and \\(x=-13\\), a physical side length cannot be negative. Therefore only 13 metres is meaningful in this context. Option C is correct. The nearby choices 12 and 14 do not work because their squares are 144 and 196, while 11 has square 121; none gives the stated area.
Frequently asked questions
What is the correct answer to this question?
(13) m
Why is this the correct answer?
The area of a square is obtained by multiplying its side by itself. If the side length is x metres, the area is \\(x^2\\) square metres. The given area is 169 square metres, so the equation is \\(x^2=169\\). We need the length whose square is 169. Since \\(13\times13=169\\), the positive length is 13 metres.
Although the algebraic equation has the solutions \\(x=13\\) and \\(x=-13\\), a physical side length cannot be negative. Therefore only 13 metres is meaningful in this context. Option C is correct. The nearby choices 12 and 14 do not work because their squares are 144 and 196, while 11 has square 121; none gives the stated area.
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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