a rectangular plot of land has an area of 1050meters squared. its length exceeds its width by 5 meters. find the length of the plot.
let the width be x m
then the length is x+5 m
so x(x+5) = 1050
now you solve it and let me know what you got.
To find the length of the rectangular plot, we can solve the quadratic equation formed by the given information.
Let's start by setting up the equation:
The area of a rectangle is equal to its length multiplied by its width.
Given that the area is 1050 square meters, and the length exceeds the width by 5 meters, we can express the length as x + 5 meters and the width as x meters.
So, the equation representing the area of the rectangle is:
x(x + 5) = 1050
Now, let's solve this equation:
Expanding the equation, we get:
x^2 + 5x = 1050
Moving all terms to one side to form a quadratic equation:
x^2 + 5x - 1050 = 0
To solve this quadratic equation, we can use factorization, completing the square, or the quadratic formula.
Using the quadratic formula:
The quadratic formula is given by x = ( -b ± √(b^2 - 4ac) ) / 2a,
where the quadratic equation is in the form ax^2 + bx + c = 0.
For this equation, a = 1, b = 5, and c = -1050. Plugging these values into the quadratic formula, we have:
x = (-5 ± √(5^2 - 4(1)(-1050))) / (2(1))
x = (-5 ± √(25 + 4200)) / 2
x = (-5 ± √(4225)) / 2
x = (-5 ± 65) / 2
We have two possible solutions:
1. x = (-5 + 65) / 2 = 60 / 2 = 30
2. x = (-5 - 65) / 2 = -70 / 2 = -35
Since we are dealing with measurements, the width cannot be negative. Hence, we discard the second solution.
Therefore, the width of the rectangular plot is 30 meters.
To find the length:
Length = Width + 5 = 30 + 5 = 35 meters
Therefore, the length of the plot is 35 meters.