Question

A square field is $40\,{\rm{m}}$ long. The perimeter of the square field is (in cm)
A) $14000\,{\rm{cm}}$
B) $16000\,{\rm{cm}}$
C) $12000\,{\rm{cm}}$
D) $8000\,{\rm{cm}}$

Answer 1

Hint: Use the formula $P = 4 \times l$, where $\left( l \right)$ is the perimeter and $\left( l \right)$is the length of the square. At last convert the answer to centimeter by multiplying with a factor ${\rm{100}}{\rm{.}}$

Complete step by step answer:
In the given question,
Side of the square $\left( l \right)$ is $40\,{\rm{m}}{\rm{.}}$
Perimeter is always considered as the sum of all the sides of an object, whether it is a square, rectangle or any shaped object. It is referred to as the length required to construct that figure. In this case it is a square and the perimeter is the sum of all the sides of the square. Since, in case of a square, all the sides are equal. So, the perimeter of the square can also be written as the product of the number of sides and the length of one side.
Let us consider perimeter be $P.$
Mathematically, it can be written as:
$P = 4 \times l$ …… (1)
By substituting, $l = 40\,{\rm{m}}$in equation (1), we get,
$\begin{array}{c}P = 4 \times l\\ = 4 \times 40\,{\rm{m}}\\{\rm{ = 160}}\,{\rm{m}}\end{array}$
Hence, the perimeter is found out to be ${\rm{160}}\,{\rm{m}}{\rm{.}}$
But the final answer is asked in centimetres, so the answer needs to be converted to meters.
We know,
$1\,{\rm{m}} = 100\,{\rm{cm}}$
So, multiply ${\rm{160}}\,{\rm{m}}$by a factor ${\rm{100}}{\rm{.}}$
So, the perimeter will be:
$\begin{array}{c}P = 160\,{\rm{m}} \times 100\,{\rm{cm }}{{\rm{m}}^{ - 1}}\\ = 16000\,{\rm{cm}}\end{array}$

Hence, the final answer is $16000\,{\rm{cm}}{\rm{.}}$

Additional information: A perimeter is a path embracing / surrounding a two-dimensional structure. The term can be used either for the direction, or in one dimension for its length. It can be viewed as the length of a form outline. In terms of geometry, it is the distance around a flat object.

Note: In this problem, we are asked to find the perimeter of the square. Here, we have multiplied the length of one side by a factor $4.$ By an alternative way, the perimeter can also be found out by adding all the sides with each other.