The length of a rectangle is 1m more than its breadth. find it's length and breadth if the area is 12
solve
x(x+1) = 12
x^2 + x - 12 = 0
it factors.
To find the length and breadth of the rectangle, we can use the formula for the area of a rectangle, which is:
Area = Length x Breadth
Given that the area is 12 and the length is 1 meter more than the breadth, we can set up an equation:
12 = (Breadth + 1) x Breadth
Simplifying the equation, we have:
12 = Breadth^2 + Breadth
Rearranging the equation to a quadratic form, we get:
Breadth^2 + Breadth - 12 = 0
We can now solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use factoring:
(Breadth - 3)(Breadth + 4) = 0
From this equation, we have two possibilities:
1. Breadth - 3 = 0 OR Breadth + 4 = 0
Breadth = 3 Breadth = -4
Since the breadth cannot be negative, we discard Breadth = -4 as a valid solution. Therefore, the breadth of the rectangle is 3 meters.
Now, we can find the length by adding 1 meter to the breadth:
Length = Breadth + 1
Length = 3 + 1
Length = 4 meters
So, the length of the rectangle is 4 meters, and the breadth is 3 meters.