The simplified area function in terms of y for a rectangle is [tex]f(y)=2 y^{2}+4 y[/tex]
Solution:
Given that length of each side of a square = y
Need to determine area of rectangle whose length is twice the length of the square and width is 2 units longer that the side length of square
Length of rectangle = twice of side length of square = [tex]2 \times y = 2y[/tex]
Width of rectangle = 2 + side length of square = 2 + y = y + 2
[tex]\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle.}[/tex]
On substituting length and width in formula for area, we get
[tex]\text { Area of rectangle }=2 y \times (y+2)=2 y^{2}+4 y[/tex]
Hence function [tex]f(y)=2 y^{2}+4 y[/tex] is represents area of required rectangle.
