Question

The sides of a square all have a side length of y. Write a simplified area function in terms of y for a rectangle whose length is twice the side length of the square and whose width is 2 units longer than the side length of the square

Answer 1

The simplified area function in terms of y for a rectangle is $f(y)=2 y^{2}+4 y$

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 = $2 \times y = 2y$

Width of rectangle = 2 + side length of square = 2 + y = y + 2

$\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle.}$

On substituting length and width in formula for area, we get

$\text { Area of rectangle }=2 y \times (y+2)=2 y^{2}+4 y$

Hence function $f(y)=2 y^{2}+4 y$ is represents area of required rectangle.