If the ratio between the length and the perimeter of a rectangular plot is 1:3 then the ratio between the length and breadth of plot is?
let the length be x
let the breadth be y
perimeter = 2x + 2y
given : length : perimeter = x : 2x+2y = 1:3
x/(2x+2y) = 1/3
3x = 2x+2y
x = 2y
length : breadth = x : y
= 2y:y
= 2 : 1
To find the ratio between the length and breadth of the plot, we need to understand the relationship between the length, breadth, and the perimeter of a rectangular plot.
Let's assume the length of the plot is L and the breadth is B. The perimeter of a rectangle is given by the formula:
Perimeter = 2(L + B)
According to the given information, the ratio between the length and the perimeter of the plot is 1:3. This means:
Length : Perimeter = 1 : 3
Substituting the values in terms of L and B:
L : 2(L + B) = 1 : 3
To obtain the ratio between the length and breadth, we rearrange the equation:
L / (2L + 2B) = 1 / 3
Now, cross multiply and solve for the ratio:
3L = 2L + 2B
3L - 2L = 2B
L = 2B
So, the ratio between the length and breadth of the plot is 2 : 1.