A rectangular paddock has an area of 240m². Find the breadth if the length is 8 meters longer than the breadth.
b(b+8) = 240
Now just solve for b
To solve this problem, let's assume the breadth of the rectangular paddock as "x" meters.
According to the problem, the length is 8 meters longer than the breadth, which means the length is (x + 8) meters.
The area of a rectangle is calculated by multiplying the length and the breadth. In this case, the area is 240m².
So, the equation representing this situation is:
Length × Breadth = Area
(x + 8) × x = 240
Now, let's solve this equation to find the value of "x" (the breadth).
x(x + 8) = 240
x² + 8x = 240
x² + 8x - 240 = 0
To solve this quadratic equation, we can factorize it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 8, and c = -240. Plugging in these values:
x = (-8 ± √(8² - 4(1)(-240))) / 2(1)
x = (-8 ± √(64 + 960)) / 2
x = (-8 ± √1024) / 2
x = (-8 ± 32) / 2
Now, we have two possible values for "x":
x₁ = (-8 + 32) / 2 = 24 / 2 = 12
x₂ = (-8 - 32) / 2 = -40 / 2 = -20
Since the breadth cannot be negative, we discard x₂ = -20 as an extraneous solution.
Therefore, the breadth of the rectangular paddock is 12 meters.
To find the breadth of the rectangular paddock, we can use the given information that the length is 8 meters longer than the breadth.
Let's assume the breadth of the paddock is 'x' meters.
According to the problem, the length is 8 meters longer than the breadth, so the length is 'x + 8' meters.
Now, the formula for finding the area of a rectangle is length × breadth.
Given that the area of the paddock is 240m², we can write the equation as:
x(x + 8) = 240.
Expanding the equation, we have:
x^2 + 8x = 240.
Rearranging the equation in standard quadratic form, we get:
x^2 + 8x - 240 = 0.
To solve this quadratic equation, we can factorize it or use the quadratic formula. Since the equation is easily factorizable, let's factorize it as:
(x + 20)(x - 12) = 0.
Setting each factor to zero and solving for 'x', we get two possible solutions:
x + 20 = 0 or x - 12 = 0.
Solving each equation, we find:
x = -20 or x = 12.
Since we are dealing with measurements, we can discard the negative value for 'x'.
Therefore, the breadth of the rectangular paddock is 12 meters.