A community is building a square garden with a walkway around the perimeter. One side is 32 ft. The area of the inner square is equal to 75% of the total area. Write and equation for the area of the inner square. One side of the inner square is x.

Question

I have been going back and forth between lessons and could only find some equations, but I don't know how to incorporate the numbers, I have tried many different combinations as well. I really need a push in the right direction. So The equation that is a base to use is ax^2+bx+c=0.
This is what I have
32x^2(3/4)=0
1024x(3/4)=0
768=0______
\ /768 (Finding the square root)
27.7128
So approximately the length of one side is 27.7 with what I used. But I am not entirely sure that this is correct. Someone please check this over and see what I possibly wrong.

Answer 1

"One side is 32 ft" is ambiguous.
Method 1
I am assuming that by "one side" you mean the side of the inside square
So the area of the square is 32^2 or 1024 ft^2

Further assumption: the walkway has the same width all around
Let the width of the walkway be x ft
So the whole thing has dimensions 32+2x by 32+2x
Area of whole thing = (32+2x)^2 = 1024 + 128x + 4x^2

75% of the whole thing = 32^2 = 1024
(3/4)(4x^2 + 128x + 1024) = 1024
3x^2 + 96x + 768 - 1024 = 0
3x^2 + 96x - 256 = 0
x = 2.475 ft, so the walkway is 2.475 ft wide

check: area of whole thing = (32 + 2*2.475)^2 = 1363.3025
and 75% of that is 1023.97... or 1024 with roundoff

Method 2.
Interpretation: The side of the original inside square is x ft
then the side of the whole thing is 32 ft by 32 ft with a total area
of 1024 ft^2
which means that the inner square is 75% of that
x^2 = .75(1024) = 768
x = √768 = appr 27.713

check: inner area = 768
outer area = 1024
is 768/1024 = .75 ? Yes it is

You pick the interpretation, state the question more clearly next time.

Answer 2

I didn't even understand what the question was saying-
xD

Answer 3

Thank you so much, that helps a lot!!!