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The perimeter of a rectangular outdoor patio is 66 ft. The length is 5 ft greater than the width. What are the dimensions of the patio?

Respuesta :

Since the perimeter us 66 ft and the length is 5 ft greater than the width, it can be said as:

66 ft = 5x ft + 5x ft + x ft + x ft

66 being perimeter, 5x being length, and x being width. This equation would then be simplified to:

66 ft = 10x ft + 2x ft
66 ft = 12x ft

Then using the simplified equation, you could then find x by dividing 66 by 12:

66 ft = 12x ft
5.5 ft = x ft

Using what has been found to be x, you would then just plug into the length and width equations:

5.5 ft = width

and

5 x 5.5 ft = 27.5 ft = length
facundo3141592

We want to find the dimensions of a patio given that we know the perimeter and the relation between the measures.

We will find that the width is equal to 14ft, and the length is equal to 19ft.

Let's see how to solve this:

Remember that for a rectangle of length L and width W, the perimeter is:

P = 2*(L + W)

We do know that the perimeter is equal to 66ft, then we have:

P = 66ft = 2*(L + W)

We also know that the length is 5ft greater than the width

L = W + 5ft

Replacing that on the perimeter equation, we get:

P = 66ft = 2*(W + 5ft + W)

Now we can solve this for W.

66ft = 2*(W + 5ft + W)

66ft = 2*(5ft + 2*W) = 10ft + 4*W

66ft - 10ft = 4*W

56ft = 4*W

56ft/4 = 14ft = W.

The width of the patio is 14ft long, and we know that the length is 5ft longer, so the length is 19ft long.

If you want to learn more, you can read:

https://brainly.com/question/3382480