Area of rectangle room is 165 sq.m. the length is 4m more than its breath and the perimeter is 52m. Find the length and breadth of the room?
To find the length and breadth of the rectangle room, we can use the given information about its area and perimeter.
Let's denote the breadth of the room as 'b' meters.
According to the information given, the length of the room is 4 meters more than its breadth, so the length can be represented as 'b + 4' meters.
Now, we can use the equations for area and perimeter to solve for unknown variables.
1. Area of rectangle = Length * Breadth
Given that the area is 165 square meters, we have the equation:
(b + 4) * b = 165
2. Perimeter of rectangle = 2 * (Length + Breadth)
Given that the perimeter is 52 meters, we have the equation:
2 * (b + b + 4) = 52
Let's solve these equations step-by-step to find the values of 'b' and 'b + 4'.
1. Area equation:
b^2 + 4b = 165
2. Perimeter equation:
2b + 8 = 52
Simplify the perimeter equation:
2b = 52 - 8
2b = 44
Solve for 'b':
b = 44 / 2
b = 22
Now, substitute the value of 'b' back into the area equation to find the length:
(b + 4) * b = 165
(22 + 4) * 22 = 165
26 * 22 = 165
572 = 165
This equation does not hold true, so there might be an error in the given information. Please double-check the problem and provide accurate information to find the length and breadth of the room.
To find the length and breadth of the room, we need to set up a system of equations based on the given information.
Let's assume the breadth of the room is x meters. Since the length is 4 meters more than the breadth, the length can be represented as (x+4) meters.
We know that the area of a rectangle is calculated by multiplying its length by its breadth. So, we have the equation:
Area = Length * Breadth
165 sq.m = (x+4) * x
Next, we know that the perimeter of a rectangle is calculated by adding all its sides. For a rectangle, this means multiplying the sum of the length and breadth by 2. So, we have the equation:
Perimeter = 2 * (Length + Breadth)
52 m = 2 * ((x+4) + x)
Now, we have a system of two equations in two variables. We can solve this system to find the values of x (breadth) and (x+4) (length).
Let's solve it:
From the first equation, we have:
165 = x^2 + 4x
Rearranging this equation, we get:
x^2 + 4x - 165 = 0
This quadratic equation can be factored or solved using the quadratic formula. Solving it, we find:
x = 11 or x = -15
Since the dimensions of a room cannot be negative, we disregard x = -15. Therefore, the breadth is x = 11 meters.
Using this value, we can find the length:
Length = x + 4 = 11 + 4 = 15 meters
Thus, the length of the room is 15 meters, and the breadth is 11 meters.
2L + 2W = 52
L = W + 4
substituting ... 2(W + 4) + 2W = 52
4W + 8 = 52