Question 340831
A diagonal drawn through square A is half as long as a diagonal drawn through square B. 
The area of square B is how many times the area of square A?
:
Establish the relationship between the diagonal and the area
Let x = the diagonal of square A
Let s = the side of square A
 s^2 + s^2 = x^2
{{{sqrt(2s^2)}}} = x
{{{s*sqrt(2)}}} = x
s = {{{x/sqrt(2)}}}
Area = s^2
A = {{{(x/sqrt(2))^2}}}
A = {{{x^2/2}}} the area of A
:
Let 2x = diagonal of B
Replace x with 2x in the above equation
A = {{{(2x)^2/2}}}
A = {{{(4x^2)/2}}}
A = {{{(2x^2)}}} is the area of B
:
Divide Area of B by the area of A
{{{(2x^2)/(x^2/2)}}}
2x^2 * {{{2/x^2}}}
Cancel x^2
2 * 2 = 4 times area of A is the area of B