Question

The area of a square plot is 144 sqm. A wire has to be put four times around this square. What is the length of the wire needed?

Answer 1

Answer :-

• The length of wire needed = 192 m.

Given :-

• The area of a square plot is 144 m².
• A wire has to be put four times around this square.

To find :-

• The length of the wire needed.

Step-by-step explanation :-

• In this question, the area of a square plot has been given to us. It has also been given that a wire has to be put four times around this square plot. For this, we are going to find the perimeter of the plot and not it's area because the wire has to be put around it, that means the wire needs to be put on the boundaries, and for this purpose, we always find the perimeter. Let's calculate our answer now!

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To find the perimeter of the square, we first have to find the length of it's each side using it's area.

We know that :-

$\underline{\boxed{\sf Area \: of \: a \: square = Side \times Side.}}$

Here,

• Area = 144 m².

Hence,

$\underline{ \underline{ \mathfrak{Substituting \: the \: given \: values,}}}$

$\longmapsto\rm144 = Side \times Side$

$\longmapsto\rm144 = {Side}^{2}$

$\longmapsto \rm\sqrt{144} = Side$

$\overline{\boxed{ \longmapsto\rm12 \: m = Side}}$

• So, the length of each side of the square plot = 12 m.

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Now let's find the perimeter of the plot!

We know that :-

$\underline{\boxed{\sf Perimeter \: of \: a \: square = 4 \times Side}}$

Here,

• Side = 12 m.

Hence,

$\underline{ \underline{ \mathfrak{Substituting \: the \: given \: values,}}}$

$\rightarrow \rm Perimeter = 4 \times 12$

$\overline{ \boxed{ \rightarrow \rm Perimeter = 48 \: m}}$

• So, the perimeter of the plot is 48 m.

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Now, finally let's find the length of the wire needed!

• The length of wire needed in one round is equal to it's perimeter.

• The perimeter here is 48 m, so the length of wire needed in one round is 48 m.

Therefore,

Length of wire needed to put the wire four times around the square plot is :-

$\rightarrow\bf48 \times 4$

$\overline{\boxed{\rightarrow\bf192 \: m}}$

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• Thus, 192 m of wire is required to cover the plot 4 times.

Answer 2

${ \green{ \boxed{ \bf \gray{SO} \bf {LU} \bf \gray{TI} \bf{ON -}}}}$

Area of square plot = 144 m²

Length of the wire = perimeter of the square plot

Since,

wire has to be put four times,

therefore,

length of the wire = 4 × perimeter of the square plot.

Now,

To find the perimeter of the plot,

we know that,

$\sf \: Area \: of \: square = (side)² \\ \longrightarrow \sf \: 144 {m}^{2} = ( {side)}^{2} \\ \longrightarrow \sf \: \sqrt{144} = side \\ \longrightarrow \sf \: 12 = side \\ \therefore \: \sf \: side = 12 \: m$

so,

$\sf \: Perimeter \: of \: square = 4 × side \\ = \sf \: 4 \times 12 \: m \\ \sf \: = 48 \: m$

Now,

$\sf \: Length \: of \: wire = 4 × perimeter \: of \: square \\ = \sf 4 \times 48m \\ \boxed{ \red{ \sf \: = 192 \: m \: \: ...ans}}$

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