Question 15 Marks
A rectangular piece of land measures $0.7 \ km$ by $0.5 \ km.$ Each side is to be fenced with $4$ rows of wires. What is the length of the wire needed ?
Answer
View full question & answer→$i.\ $From the given figure, the side of one slab is $\frac{1}{2} m$
Therefore, the side of the square formed by Avneet $=\left(3 \times \frac{1}{2}\right) m=\frac{3}{2} m$
Now,
We know that the perimeter of a square $= 4 \times$ Side $=4 \times \frac{3}{2}=6 \mathrm{m}$
$ii.\ $We know that,
Perimeter $=$ Sum of all sides
Therefore Perimeter of the Shari's arrangement $= 0.5 + 1 + 1 + 0.5 + 1 + 1 + 0.5 + 1 + 1 + 0.5 + 1 + 1 = 10 m$
$iii.\ $The arrangement which is in the shape of the cross has a greater perimeter $($i.e. $10 m)$
$iv.\ $If we put all $9$ slabs in a line then, the perimeter will be $10 m,$ as shown below.
Thus, from the given arrangements, arrangements with perimeters greater than $10 m$ cannot be determined.
Hence $10$ is the largest possible value if the perimeter.
Therefore, the side of the square formed by Avneet $=\left(3 \times \frac{1}{2}\right) m=\frac{3}{2} m$
Now,
We know that the perimeter of a square $= 4 \times$ Side $=4 \times \frac{3}{2}=6 \mathrm{m}$
$ii.\ $We know that,
Perimeter $=$ Sum of all sides
Therefore Perimeter of the Shari's arrangement $= 0.5 + 1 + 1 + 0.5 + 1 + 1 + 0.5 + 1 + 1 + 0.5 + 1 + 1 = 10 m$
$iii.\ $The arrangement which is in the shape of the cross has a greater perimeter $($i.e. $10 m)$
$iv.\ $If we put all $9$ slabs in a line then, the perimeter will be $10 m,$ as shown below.
Thus, from the given arrangements, arrangements with perimeters greater than $10 m$ cannot be determined.
Hence $10$ is the largest possible value if the perimeter.