A piece of wire 5 inches long is to be cut into two pieces. One piece is x inches long and is to be bent into the shape of a square. The other piece is to be bent into the shape of a circle. Find an expression for the total area made up by the square and the circle as a function of x. HELP!!

Question

anonymous · Answer

if one piece is x inches and bent into a square, that square has 4 sides of length (x/4)

The area of that square would be (x/4)^2.

The other piece is then of length (5 - x) and is a circle with perimeter (5 - x).

Perimeter Formula : pi * d = (5-x)
Area Formula [in terms of d]: A = pi*(d^2/4)

d = (5-x)/pi

A = (pi/4)*[(5-x)/pi]^2 - can be simplified a bit

anonymous · Answer

the total area is the sum of the two

anonymous · Answer

Thank you very much!!

anonymous · Answer

glad i could help :)

lmk if you have follow up questions