how do you asnwer this math question?

Question

If one side of a square is increased by 12 feet and an adjacent side is decreased by three feet, a rectangle is formed whose perimeter is 64 feet. Draw a diagram and find the length of the side of the original square. Write an equation and solve it. Be sure to define the variables you use.

Answer 1

x = a length of a square

first draw the square with an x on all sides sides.

then change one"x" to "x + 12" (and do the same thing to the opposite side)
Then change the other "x"s to "x - 3"

since 64 is the total perimiter of the rectangle (and the perimeter is the total of the sides) all of the sides must add up to 64.
So your equation would be 64 = 4x + 18
(the "4x" is the total x's and the "18" comes from 12 + 12 - 3 - 3)

Then you work it out.
64 = 4x + 18
(64 - 18) = 4x + (18 - 18)
46 = 4x
46 / 4 = (4 / 4) x
11.5 = x

I hope this helps.

Answer 2

The problem tells you that originally you have a square, which means that all sides are equal. It also tells you that the perimeter is equal to 64, and as you may know the formula for perimeter is the sum of all sides. So we begin by calling all four sides x. which means that one of the sides will be (x-12) and the other (x-3) Since the perimeter is 64 we apply the formula and get that:
64=2(x+12)+2(x-3)
manipulating the equation we expand it to:
64=2x+24+2x-6
putting the x together
64=4x+18
We leave the x on one side and the numbers on the other and get:
4x=64-18
This gives:
4x=46
Dividing both sides by 4 to leave the x alone we get:
x=11.5
So the original square had four sides of 11.5 ft.

Answer 3

Let x = the original length of one side of the original square.

Let p= the perimeter of the rectangle

Let l= length and w = width of the rectangle

Since p = 2l + 2W, and 2l = x+24, and 2w = x-6, and p = 64 therefore:

2x + 24 + 2x - 6 = 4x + 18 to solve for x the equation is thus 4x + 18 = 64

subtract 18 from both sides 4x = 46

divide 4 on both sides x = 11.5

Conclusion the side of the original square is 11.5 feet.

Answer 4

s = one side of the square
(s+12) & (s-3) are the sides of the rect
64 = 2*((s+12)+(s-3))
64=4s+18
4s=46
s=11,5