the lenght of a rectangle is twice its breadth. if its perimeter is 18cm, find its length and breadth
P = 2L + 2W
18 = 2(2W) + 2W
18 = 6W
3 = Width (breadth)
To solve this problem, we can use the formulas for the perimeter of a rectangle and the relationship between the length and breadth.
Let's denote the breadth of the rectangle as "b" cm. According to the problem, the length of the rectangle is twice its breadth, so the length can be written as "2b" cm.
The perimeter of a rectangle is given by the formula P = 2(l + b), where P is the perimeter, l is the length, and b is the breadth.
Substituting the given information into the formula, we have:
18 = 2(2b + b)
Simplifying the equation:
18 = 2(3b)
18 = 6b
Dividing both sides of the equation by 6:
b = 3
Therefore, the breadth of the rectangle is 3 cm.
To find the length, we can substitute the value of b back into the equation:
l = 2b = 2(3) = 6
Therefore, the length of the rectangle is 6 cm.
In conclusion, the length of the rectangle is 6 cm and the breadth is 3 cm.