Ratio of height to new height = height:new height = 147/30.5 = 4.82
This is a ratio problem and not a proportion problem.
Ratio is the answer obtained by dividing two similar quantities (quantities with same units). We use symbol
: to specify ratio.
Equality of two ratios is...

a) Easiest way to solve this problem is to remember that a2 - b2 = (a+b) (a-b) and recognize the pattern from the problem
100x2-1 = (10x)2 - (1)2 = (10x+1)(10x-1)
b) If you do not remember the formula for a2 - b2, then you will need to solve the problem by using usual factoring method...

1) Yes.
xy = 3 is a rectangular hyperbola.
This hyperbola lies in first and third quadrant.
Its asymptotes are x-axis (y = 0) and y-axis (x = 0).
Center: (0,0)
Transverse axis of symmetry: y=x
Domain: set of all real numbers except x=0
Vertices: (sqrt(3), sqrt(3))...