Problema Solution
you are given a sheet of paper and told to cut out a rectangular piece with an area of (4x squared-44x+121)mm squared. the dimensions of the rectangle have the form ax-b, where a and b are whole numbers. find an expression for the perimeter of the rectangle you cut out. find the perimeter when x=41 mm.
Answer provided by our tutors
4x^2-44x+121 = (2x)^2 - 2*2x*11 + 11^2 = (2x - 11)^2
The dimensions of the rectangle have the form ax-b and knowing that the area is (2x - 11)^2 we conclude that the rectangle is square with side's length equal to 2x - 11.
The perimeter is:
P = 4*(2x - 11)
P = 8x - 44
For x = 41 mm we have:
P = 8*41 - 44
P = 328 - 44
P = 284 mm
The perimeter is 284 mm.