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When each side of a square was reduced by 2 metre the area became 49 square meters. What was the length of the side of the original square?

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Last updated date: 13th Jul 2024
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Answer
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Hint: In this type of question we have to use the concept of area of a square. Here we consider the unknown value to be equal to x and then by using formula for area of a square we will obtain the result. We know that, the area of the square is given by, \[{{\left( Side \right)}^{2}}\].

Complete step by step answer:
Now, we have to find the length of the side of the original square and given that, when each side of the square gets reduced by 2 meter the area becomes 49 square meters.
Let us suppose that the length of each side of the original square is \[x\text{ meter}\]. When each side of the square gets reduced by 2 meter, each side of the new square is \[\left( x-2 \right)\text{ meter}\].
As we know that, \[\text{Area of a square = }{{\left( Side \right)}^{2}}\]
And also we have given that, when each side of a square was reduced by 2 metre the area became 49 square meters.
\[\begin{align}
  & \Rightarrow \text{Area of a square = }{{\left( Side \right)}^{2}} \\
 & \Rightarrow \text{49 square meter = }{{\left( x-2 \right)}^{2}} \\
\end{align}\]
By taking square root of both sides we can write,
\[\begin{align}
  & \Rightarrow \pm 7=\left( x-2 \right) \\
 & \Rightarrow 7=\left( x-2 \right)\text{ and }-7=\left( x-2 \right) \\
\end{align}\]
On simplifying we get,
\[\begin{align}
  & \Rightarrow 7+2=x\text{ and }-7+2=x \\
 & \Rightarrow x=9\text{ and }x=-5 \\
\end{align}\]
But we know that the length of a square cannot be negative
\[\Rightarrow x=9\text{ meter}\]
Hence, the length of each side of the original square is 9 meter.

Note: In this type of question students have to remember the formula for the area of a square. Also students have to note that when we consider the square root of any number we have to consider both positive as well as negative values. Students have to note that the value of the side cannot be negative and hence they have to accept only positive value as a result.