A70 meter path surrounds a rectangular garden. the width of the garden is two thirds it's length. find its area

You can set up an equation.
Let x = measure of the length.

Width: 2/3x
Length: x

From the question, we know that the perimeter is 70 and based on our prior knowledge, we know that for a rectangle, the perimeter is equal to 2 times the length added to two times the width.

2(2/3x + x) = 70
4/3x + 2x = 70
10/3x = 70
x = 21

So the length is 21 meters.
And since the width is 2/3 the length, 2/3 x 21 is 14.
So the width is 14 meters.

And if you add 21 + 21 + 14 + 14, it will equal 70 meters.

Now let's find the area.
21 x 14 = 294 square meters.