Question

the wire needed, for four rounds of fencing around a rectangular ground of length 235 m, is 3.2 km. What is the breadth of the ground.

options :

(1) 165 m ,
(2) 155m ,
(3) 175m ,
(4) 170m

Answer 1

$\bold{given : } \\ \\ for \: fencing \: a \: ground \: \\ \\ needed \: wire : \\ \\ 3.2 \times 1000 \: m \: \\ \\ \bold{3200 \: m \: }$$it \: is \: 4 \: times : \: \\ \\ \: thus \: perimeter \: of \: that \: ground : \frac{3200}{4} \: m \: \\ \\ \: \bold{800 \: m \:} \\ \\ \\ \\ \bold{length \: of \: ground : }$$235 \: m \: \\ \\ \\ \\\bold {perimeter \: we \:have\: calculated =} \\ \\\bold{\: perimeter \:of \: that \: ground \:from\: formula}$$\\ \\ 800 \: m \: = \: 2 \: ( \: l \: + \: b \: ) \\ \\ 800 \: = 2l \: + \: 2b \\ \\ 800 = 2 \times 235 + 2b \\ \\ 800 = 470 + 2b \\ \\ 2b = 800 \: - 470 \\ \\ 2b \: = \: 330 \\ \\ b \: = \: \frac{330}{2}$$\\ \\ \bold{b \: = 165 \: m \: } \: \\ \\ \\ \\ \: \bold{breadth \: of \: the \: rectangle : } \\ \\ \bold{165 \: m \: }$

Answer 2

Length Of Ground=235 m
LET Breadth of ground=X m
Perimeter=2(l+B)
=2(235+x)
=470+2x m

MEANS in 1 round it complete fencing of (470+2x)m

In 4 rounds
4(470+2x)
=(1880+8x)m

In 4 round it completed=3.2 km=3200 m
Then,
1880+8x=3200
8x=3200-1880
8x=1320
X=1320/8
x=165 m

So Breadth=165 m
$\boxed{\mathbf{Breadth=165 m}}$