Question

The length and breadth of a rectangular field are 4 m and 3 m respectively. The field is divided into two
parts by fencing diagonally. The cost of fencing at the rate of ₹10 per metre is

(a) ₹50 (b) ₹30 (c) ₹190 (d) ₹240

Answer 1

Let l and b be the length and breadth of the rectangle respectively. Then
l = 4 m and b = 3 m
Now, in the triangle formed by the adjacent sides and one diagonal of the rectangle, using Pythagoras theorem, we have
l² + b² = (Diagonal)²
$\Rightarrow$ (Diagonal)² = 4² + 3² = 16 + 9 = 25
$\Rightarrow$ Diagonal = 5 m
Length of fencing = 2(l + b) + Length of diagonal
= 2(4 + 3) + 5
= 14 + 5
= 19 m
Cost of fencing = ₹10 $\text{×}$ 19 = ₹190
Hence, the correct option is (c).