Question

Consider a square field ABCD. The diagonal AC is 50 meter. The cost of laying grass in the field is Rs. 5 per square-meter. The total cost for laying grass in the field ABCD is Rs. ________ (rounded off to two decimal places).

Hint:

To find the area of a square when the diagonal is given, use the Pythagorean theorem: \( {Diagonal}^2 = 2 \times {Side}^2 \).

Answer 1

Step 1: Use the given information to find the side length of the square.

In a square, the diagonals are equal in length, and they bisect each other at right angles. Let \( s \) be the side length of the square. Using the Pythagorean theorem for the right triangle formed by two sides of the square and the diagonal, we have:
\[ \text{Diagonal}^2 = s^2 + s^2 \] Since the length of the diagonal AC is given as 50 meters: \[ 50^2 = 2s^2 \quad \Rightarrow \quad 2500 = 2s^2 \quad \Rightarrow \quad s^2 = 1250 \] \[ s = \sqrt{1250} = 35.36 \, \text{meters} \quad (\text{rounded to two decimal places}). \] Step 2: Find the area of the square.

The area \( A \) of the square is given by: \[ A = s^2 = 1250 \, \text{square meters}. \] Step 3: Calculate the total cost of laying grass.

The cost of laying grass is Rs. 5 per square meter. So, the total cost is: \[ \text{Total cost} = 1250 \times 5 = 6250 \, \text{Rs}. \] Step 4: Final answer.

The total cost for laying grass in the field ABCD is Rs. 6250.00.