One side of a rectangular field is 15 m, and the length of its diagonal is 17 m. Using this information, find the area of the rectangular field in square metres (m^2).

Introduction / Context:
This question tests how to use the Pythagoras theorem in a rectangle. In any rectangle, the diagonal, length, and breadth form a right-angled triangle. If you know one side and the diagonal, you can find the other side and then compute the area as length * breadth.

Given Data / Assumptions:

• One side of the rectangle = 15 m
• Diagonal of the rectangle = 17 m
• Let the unknown other side be = x m
• Area of rectangle = (one side) * (other side)

Concept / Approach:
Use Pythagoras theorem on the right triangle formed by the sides and diagonal: diagonal^2 = side^2 + other_side^2. Then compute area = side * other_side.

Step-by-Step Solution:
17^2 = 15^2 + x^2 289 = 225 + x^2 x^2 = 289 - 225 = 64 x = 8 m Area = 15 * 8 = 120 m^2

Verification / Alternative check:
If the sides are 15 m and 8 m, the diagonal should be sqrt(15^2 + 8^2) = sqrt(225 + 64) = sqrt(289) = 17 m, which matches the given diagonal.

Why Other Options Are Wrong:
110 m^2: would require the other side to be 110/15 = 7.33 m, not consistent with the diagonal 17 m. 130 m^2: would require the other side to be 8.67 m, changing the diagonal. 140 m^2: would require the other side to be 9.33 m, changing the diagonal. 150 m^2: would require the other side to be 10 m; then diagonal becomes sqrt(15^2 + 10^2), not 17.

Common Pitfalls:
Forgetting that the diagonal with the sides forms a right triangle. Squaring incorrectly (mixing up 17^2 and 15^2). Finding the missing side but forgetting area needs multiplication of the two sides.

Final Answer:
Area of the field = 120 m^2