SOLUTION: Paula is building a rectangular patio. It will have a square flower bed in the middle. The rest will have paving stones. The patio will have a length of Ax and a width of 3.1x.

Question 1191230: Paula is building a rectangular patio. It will
have a square flower bed in the middle. The
rest will have paving stones. The patio will
have a length of Ax and a width of 3.1x. The
area of the flower bed will be 3.52. What
area of the patio will need paving stones?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
capital A is usually used to represent area.
in this case, i think it might represent the area of the flower bed.
assuming i'm right, i think the solution to this problem might be as follows:

length of the patio is Ax.
width of the patio is 3.1x.

length and width of the flower bed is x.
the area of the flower bed is 3.52 which is equal to x^2.
this makes x = sqrt(3.52).

length of the patio is Ax = 3.52x
width of the patio is 3.1x.
area of the patio is 3.52x * 3.1x = 10.912x^2

since x = sqrt(3.52), then area of the patio is equal to 10.912 * x^2 = 10.912 * 3.52 = 38.41024.

the area of the patio that will need paving stones will be 38.41024 minus 3.52 = 34.89024.

that's what i think if my assumption about the value of A is correct.

if i did not know the value of A, then i would have done the following:

area of the patio = Ax * 3.1x = 3.1Ax^2
area of the flower bed = 3.52 = x^2
area of the patio becomes 3.1 * A * 3.52 = 10.912A

area of the patio that needs to be paved would be equal to 10.912A - 3.52.
i would not know the value of A and could not make any assumptions about its value.

my assumption that A is equal to the area of the flower bed gave it a value.
if i was right, then your answer would be that the area of the patio that will need paving stones will be 38.41024 minus 3.52 = 34.89024.
if i was wrong, then i would have to stick with the area of the patio that will need paving stones will be equal to 10.912A - 3.52.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

The solution and the answer to this problem are in one line

        the area of the patio which should be paved is (Ax)*(3.1x) - 3.52 = 3.1Ax^2 - 3.52.             ANSWER

The many-word reasoning in the post by @Theo, his solution and his answer are incorrect and irrelevant.

Ignore his post, for the peace in your mind.

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