ratio question to increase in area

Question

a rectangular area whose length to width ratio is 3 to 2.  if 3 times as much material is used for rectangle area, but the ratio is maintained, which describes the increase in enclosed area?

Choices:

A.)  2 to 4 times larger

b.)  5 to 7 times larger

c.)  8 to 10 times larger

d.) 11 to 13 times larger

Answer 1

Let x be the width then length=3x/2. Area=3x²/2. 

Perimeter=2(x+3x/2)=5x. If 3 times as much material is used to make the rectangle, the perimeter increases to 15x. The width becomes 3x and the length 9x/2 so the area becomes 27x²/2.

So this new area is 9 times the original area (9=3²) so the answer is c.