the width of a rectangle is two thirds its length. if the perimeter is 180 meters find the rectangle.

let the width of the rectangle be k.

so the length of rectangle is (3/2)k.
Perimeter of the rectangle=(3/2)k+(3/2)k+k+k
=5k
=180m
so,
5k=180
k=36.
thus,
the width of the rectangle is 36m.
For the length,
Length=(3/2)(36)
=54m

P = 2L + 2W

180 = 2L + 2(2/3)L

180 = 2 4/3L

180 / (10/3) = L

180 * (3/10) = L

540/10 = L

54 = L

To find the dimensions of the rectangle, we can set up equations based on the given information.

Let's assume the length of the rectangle is "L" meters.
According to the given information, the width of the rectangle is two-thirds its length. Therefore, the width can be calculated as (2/3) * L.

Moreover, the perimeter of a rectangle is given by the formula P = 2(L + W), where P is the perimeter, L is the length, and W is the width.

In this case, the perimeter is 180 meters. So, we can write the equation as:

180 = 2(L + (2/3) * L)

To solve for L, we need to simplify the equation:

180 = 2(L + 2/3 * L)
180 = 2(5/3 * L)
180 = (10/3) * L
L = (180 * 3) / 10
L = 54 meters

Now, we can find the width using the formula:

Width = (2/3) * L
Width = (2/3) * 54
Width = 36 meters

Therefore, the rectangle has a length of 54 meters and a width of 36 meters.