The difference between the length and the breathe of a rectangle is 12 m.the perimeter of a rectangle is 144m.find the dimensions.
breath (width) ---- x
length -----------x+12
2x + 2(x+12) = 144
carry on
To solve this problem, we can set up a system of equations based on the given information.
Let's say the length of the rectangle is L and the breadth is B.
According to the problem, the difference between the length and the breadth is 12m. So we can write the equation:
L - B = 12 ----(Equation 1)
Also, it is given that the perimeter of the rectangle is 144m. The formula for the perimeter of a rectangle is:
Perimeter = 2 * (Length + Breadth)
Using this formula and substituting the values, we get:
144 = 2 * (L + B)
Dividing both sides of the equation by 2, we have:
72 = L + B ----(Equation 2)
Now, we have a system of equations with Equation 1 and Equation 2.
Next, we can solve this system of equations using any method like substitution or elimination.
Let's solve using the substitution method.
From Equation 1, we can express L in terms of B:
L = B + 12
Now substitute this value of L in Equation 2:
72 = (B + 12) + B
Simplifying the equation:
72 = 2B + 12
Subtracting 12 from both sides:
60 = 2B
Dividing both sides by 2:
B = 30
Now substitute this value of B in Equation 1:
L - 30 = 12
Adding 30 to both sides:
L = 42
Therefore, the dimensions of the rectangle are:
Length (L) = 42 meters
Breadth (B) = 30 meters
To find the dimensions of the rectangle, let's assign variables to the length and breadth.
Let the length be L and the breadth be B.
According to the given information, the difference between the length and breadth of the rectangle is 12 meters. Mathematically, this can be represented as:
L - B = 12
Also, the perimeter of a rectangle is given as 144 meters. The formula for calculating the perimeter of a rectangle is:
Perimeter = 2 * (Length + Breadth)
Substituting the values, we get:
144 = 2 * (L + B)
Simplifying the equation further:
72 = L + B
Now, we have a system of two equations:
Equation 1: L - B = 12
Equation 2: L + B = 72
We can solve this system of equations using different methods such as substitution, elimination, or graphical methods. Let's solve it using the elimination method:
Adding both equations, we get:
(L - B) + (L + B) = 12 + 72
2L = 84
L = 42
Now, substitute the value of L into one of the equations:
42 + B = 72
B = 30
So, the dimensions of the rectangle are length = 42 meters and breadth = 30 meters.