The diagonal and the longer side of a rectangular plot are together three times the length of the shorter side. If the longer side exceeds the shorter side by 140 feet, what is the area of the plot?
To find the area of the plot, we need to determine the dimensions of the rectangular plot. Let's proceed step-by-step.
Let's assume the shorter side of the rectangular plot is denoted as 'x' feet.
According to the given information, the longer side of the rectangular plot exceeds the shorter side by 140 feet. Therefore, the longer side can be expressed as 'x + 140' feet.
It is also mentioned that the diagonal and the longer side of the plot together are three times the length of the shorter side.
Using the Pythagorean theorem, we know that the square of the length of the diagonal of a rectangle is equal to the sum of the squares of its length and breadth.
In this case, we have the following equation:
(diagonal)^2 = (shorter side)^2 + (longer side)^2
As the diagonal is not given, we cannot directly solve for the dimensions. However, we can construct another equation to help us solve the problem.
It is given that the diagonal and the longer side together are three times the length of the shorter side. This can be expressed as:
diagonal + longer side = 3 * shorter side
Substituting the values of the dimensions, we have:
diagonal + (x + 140) = 3x
Rearranging the equation, we get:
diagonal = 3x - (x + 140)
diagonal = 2x - 140
Now we have two equations:
(diagonal)^2 = (shorter side)^2 + (longer side)^2
diagonal = 2x - 140
Simplifying the first equation, we have:
(2x - 140)^2 = x^2 + (x + 140)^2
Expanding and solving the equation will give us the value of x, which represents the length of the shorter side.
Once we have the dimensions (length and width) of the rectangular plot, we can calculate the area by multiplying the length by the width.
I hope this explanation helps you understand the steps required to solve the problem.