We can simplify by reducing factors between the 5 and the 50, as well as between the 42 and the 3.
Response:
$54
Detailed steps to explanation:
Initially
45 multiplied by.05 equals 2.25
Next
45 added to 2.25
Following that
45 multiplied by.15 equals 6.75
Finally
45 plus 2.25 plus 6.75
Response: a) 
b) The area has grown by 0.75 square meters.
Detailed breakdown:
Let the room's length be l
Let the room's breadth be 'b'
The area of a rectangle is calculated using the formula:

Per the problem, the room's new area equals 175% of its old area.
Thus, a) The new area of the room is determined as

This indicates a 175% increase in the room's length, resulting in a 175% increase in area.
b) The increase in square meters for Megan's room area is

A 40-degree angle may be applicable for this question