a rectangle has a length of 17 inches more than twice its height. If the perimeter of a rectangle is 304 inches, find its dimensions.

P = 2L + 2H

304 = 2(2H + 17) + 2H

304 = 6H + 34

270 = 6H

45 = H

107 = L

To find the dimensions of a rectangle with a given perimeter, we need to set up equations based on the information provided.

Let's assume the height of the rectangle is "h" inches.
According to the problem, the length of the rectangle is 17 inches more than twice its height. So the length can be represented as (2h + 17) inches.

The formula for calculating the perimeter of a rectangle is: Perimeter = 2 * (length + height)

Substituting the given values into the formula, we get:
304 = 2 * ((2h + 17) + h)

Simplifying the equation:
304 = 2 * (3h + 17)
304 = 6h + 34
6h = 304 - 34
6h = 270
h = 270 / 6
h = 45

Now that we have the height (h = 45), we can calculate the length by substituting this value back into our earlier expression for the length:
Length = 2h + 17
Length = 2*45 + 17
Length = 90 + 17
Length = 107

Therefore, the dimensions of the rectangle are:
Height = 45 inches
Length = 107 inches