Question

A square piece of land has area 112 m${}^2$. What is the closest integer which approximates the perimeter of the land?

Answer 1

If $l$ is the side-length of a square, its perimeter is $4l$. We know that $l^2$ = $112$. Hence,
$(4l{)}^2=16l^2=(16)\times (112)=1792.$
But ${42}^2=1764<1792<1849={43}^2$ and $1764$ is nearer to $1792$ than $1849$. Hence the integer approximation for $\sqrt{1792}$ is $42$. The approximate value of the perimeter is $42$ cm.