How would you solve this?

Question

A plece of wire 46 inches long is cut into two pieces and each piece is bent into a square. If x denotes the length (in inches) of the first piece, express the total area A enclosed by both squares (sq.in.) in terms of .

Answer 1

I want you to imagine you are holding this wire and are preparing to cut off a piece. You have a wire of length 46 in you hand. You cut off an unknown amount, let's call it x and put it over to the side. The original wire in your hand is now 46 - x long. So one piece of wire is x long and the other piece is 46-x long. Each wire is to be formed into a square so the four sides of each square are 1/4 the length of the wire.

X wire each side is x/4 and you should be able to determine a formula for the area (multiplying two sides together) (x/4)(x/4)

46-x wire each side is the same length so would be (46-x)/4 for each side. You should be able to express the are for this by multiplying two sides. ((46-x)/4)((46-x)/4)

Simplify and find a total

Answer 2

If the length of the 1st piece is x, the length of the 2nd piece is (46 - x). (Those two expressions sum to 46.)

Then, both lengths are bent into 4 equal side lengths, so dividing each by 4 will give the side length of each square: x/4 and (46 - x) / 4.

Lastly, the area of a square is given by A = s² , so A₁ = x²/16 and A₂ = (46 - x)² / 16

total area = (2x² - 92x + 2,116) / 16 or 1/8x² - 23/4x + 529/4

Answer 3

A = (x/4)² + [(46 - x)/4]²

Answer 4

If 46 is the length of the wire and it is cut into a wire that is x long and one that is y long, than we know 46 the total length is = x+y. So to write the length y of the second wire in terms of x we can write that the length of the 2nd wire is 46-x=y. So the length of the first wire is x long, and the length of the second wire is 46-x long. If you bend a wire into 4 equal sides of a square, the total length divided by 4 is x/4, the length of one side. Using the formula Area= Side² we can square x/4 to find the area of the first square. The area of the second square is similarly ((46-x)/4)² The total area is these two values added.