a rectangular garden has a perimeter of 140m.its width is three quarter of its length.

what is the length and width?

Also, your spelling of "Public" is incorrect.

2L + 2 W = 140

W = (3/4)L

2L + (3/2)L = 140
(7/2)L = 140
L = (2/7)*140 = 40 m
W = 30

Let's proceed step-by-step to solve the problem.

Step 1: Assign variables
Let's assign variables to the length and width of the rectangular garden.
Let the length be "L" and the width be "W".

Step 2: Create equations
From the given information, we know that the perimeter of the garden is 140m.
Perimeter of a rectangle = 2 * (length + width)
So, we can create the equation: 2 * (L + W) = 140

We also know that the width is three-quarters (3/4) of the length.
Therefore, we can create another equation: W = (3/4) * L

Step 3: Solve the equations
Let's use the equations to find the values of L and W.

From Equation 2, we can express W in terms of L:
W = (3/4) * L

Substitute this expression for W in Equation 1:
2 * (L + (3/4) * L) = 140

Simplify the equation:
2 * (7/4) * L = 140
(14/4) * L = 140
(7/2) * L = 140

Now, isolate L by dividing both sides of the equation by (7/2):
L = 140 / (7/2)
L = 140 * (2/7)
L = 40

So, the length of the garden is 40m.

Step 4: Calculate the width
Now that we know the length, we can substitute this value into Equation 2 to find the width:
W = (3/4) * L
W = (3/4) * 40
W = 30

Therefore, the width of the garden is 30m.

Step 5: Final answer
The length of the rectangular garden is 40m and the width is 30m.

To find the length and width of the rectangular garden, we need to set up a system of equations.

Let's let "L" represent the length of the garden and "W" represent the width of the garden.

From the information given, we know that the perimeter of the rectangular garden is 140m. The perimeter of a rectangle is calculated by adding all four sides, so we can write the equation as:

Perimeter = 2(Length + Width)

Substituting in the values, we have:

140 = 2(L + W)

Furthermore, it is given that the width is three-quarters (3/4) of the length. This can be written as:

W = (3/4)L

Now we have a system of two equations:

140 = 2(L + W)
W = (3/4)L

We can solve this system of equations by substitution or elimination. Let's use substitution here:

Substitute the value of W from the second equation into the first equation:

140 = 2(L + (3/4)L)

Simplify by multiplying:

140 = 2(7/4)L

Now multiply across:

140 = (14/4)L

Simplify the fraction:

140 = (7/2)L

To eliminate the fraction, multiply both sides of the equation by 2/7:

(140)(2/7) = L

Solve for L:

L = 40

Now we can substitute the value of L back into the equation for W:

W = (3/4)(40)
W = 30

Therefore, the length of the rectangular garden is 40m and the width is 30m.