I created this problem and wanted to check my answers with the MathForum.

x = length

y = width

Scenario:

There are two Kindles.

K(1) has the dimensions of 3.6 in by 4.8 in. with a surface area (SA) of $\displaystyle 17.28in^2$ and a diagonal that measures 6 in

K(2) has the dimensions of 5.4 in by 7.9 in. with a surface area of $\displaystyle 42.66in^2$ and a diagonal that measures 9.56 in

a. How much bigger is K(2)'s SA compared to K(1)'s SA?

my answer: ~2.47 times

b. Write an equation that represents the maximum and minimum value of

x and y when the SA of K(3) is 42.66 in.

my answer: Either $\displaystyle x=42.66*y$ or $\displaystyle y=42.66*x$

Note: For 'c' I want to know if it's possible to have a minimum and maximum value of the length and width when the diagonal is 6 in. My guess is that you can only have 1 combination of 'x' and 'y' that gives you a SA of 42.66 and a diagonal of 6 in.

c. Write an equation/system of equations that represents the maximum and minimum value of x and y if the diagonal of K(3) is 6 inches.

my answer: $\displaystyle x^2 + y^2 = (6)^2$ --> y = -X + 6 (If I simplified that right) and $\displaystyle x=42.66*y$ or $\displaystyle y=42.66*x$; where the two lines intersect is the value of x and y when the diagonal is 6.