Question

The area of a square plot is 1600 m². Find the
length of wire, which can go 4 times around the
boundary of this plot.
(a) 150 m
(b) 200 m
(C) 640 m
(d) 260 m​

Answer 1

Answer:

Option (C) 640 m

The length of the wire is 640 m.

Step-by-step explanation:

Given:

Area of the square plot = 1600 m²

To find:

The length of the wire which can go 4 times around the boundary of the plot.

Solution :

Area of the Square = Side × Side

Let the side be y

$\sf{\longrightarrow} \: y \times y = 1600$

$\sf{\longrightarrow} \: {y}^{2} = 1600$

$\sf{\longrightarrow} \:y = \sqrt{1600}$

$\sf{\longrightarrow} \:y = 40$

Side = 40 m

Perimeter of square = Side × 4

$\sf{\longrightarrow} \:40 \times 4$

$\sf{\longrightarrow} \:160 \:$

Perimeter = 160 m

The wire needs to go around the boundary 4 times.

Length of the wire = Perimeter × 4

$\sf{\longrightarrow} \:160 \times 4$

$\sf{\longrightarrow} \:640$

Length of the wire = 640 m

Therefore, the length of the wire is 640 m.

Answer 2

Answer:

Given :-

• The area of a square plot is 1600 m².

To Find :-

• What is the length of wire which can go 4 times around the boundary of plot.

Solution :-

Given :

• Area = 1600 m².

First, we have to find the side of a square plot,

As we know that,

${\underline{\boxed{\mathcal{\pmb{\quad Area\: of\: Square =\: Side \times Side\quad}}}}}$

Then, according to the question,

↦ $\sf Side \times Side =\: 1600$

↦ $\sf {(Side)}^{2} =\: 1600$

↦ $\sf Side =\: \sqrt{1600}$

➦ $\sf\bold{Side =\: 40\: m}$

Hence, the each side of a square plot is 40 m .

Again, we have to find the perimeter of a square plot,

As we know that,

${\underline{\boxed{\mathcal{\pmb{\quad Perimeter =\: 4 \times Side\quad}}}}}$

Given :

• Side = 40 m

Then,

↦ $\sf Perimeter\: =\: 4 \times 40$

➦ $\sf\bold{Perimeter =\: 160\: m}$

Hence, the perimeter of a square plot is 160 m .

Now,

⇒ $\sf Length\: of\: round\: wire =\: 160\: \times 4$

➠ $\sf\bold{\red{Length\: of\: round\: wire =\: 640\: m}}$

$\therefore$ The length of wire which can go 4 times around the boundary of the plot is 640 m .