A rectangle has a perimeter of 34 cm. if 2/3 of its length is equal to 3/4 of its width. find the dimensions of the rectangle.

Perimeter of the rectangle = 34 cm

Let us assume the length of the rectangle = x

Let us assume the width of the rectangle = y

Then

Width of the rectangle can be determined by the equation

2x/3 = 3y/4

2x * 4 = 3y * 3

8x = 9y

x = (9y) / 8

Now

Perimeter of the rectangle = 2 (length + width)

34 = 2 (x + y)

34/2 = x + y

x + y = 17

Now let us put the value of x in terms of y in the second equation

x + y = 17

(9y/8) + y = 17

(9y + 8y) / 8 = 17

17y = 17 * 8

y = (17 * 8) / 17

= 8 cm

Now let us put the value of y in the equation

x + y = 17

x + 8 = 17

x = 17 - 8

= 9 cm

So the length of the rectangle is 9 cm and the width of the rectangle is 8 cm.