A rectangular plot has a concrete path running inner side of the plot is used as a lawn, which has an area of 432 sq.m. If the width of the path is 4 m and the length of the plot is greater than its breadth by 2m, what is the area of the rectangular plot? 980 m^2 975 m^2 984 m^2 960 m^2

Let's denote the length of the plot as L and the breadth as B. According to the problem, we know that:

L = B + 2 (since the length is greater than the breadth by 2m)

The area of the lawn is given as 432 sq.m. The lawn is the inner part of the plot, so its dimensions are (L - 24) and (B - 24) (since the path is 4m wide on all sides). Therefore, we can write the area of the lawn as:

(L - 8) * (B - 8) = 432

Substitute L = B + 2 into the equation:

(B + 2 - 8) * (B - 8) = 432 (B - 6) * (B - 8) = 432 B^2 - 14B + 48 = 432 B^2 - 14B - 384 = 0

Solving this quadratic equation for B, we get B = 24 or B = -16. Since B cannot be negative, B = 24m.

Substitute B = 24 into L = B + 2, we get L = 26m.

Therefore, the area of the rectangular plot is L * B = 26 * 24 = 624 sq.m.

However, none of the options match this result. There might be a mistake in the problem or the options provided.