Rectangle A has a length of 64 inches and a width of
48 inches. Rectangle B has a length and a width that
are both \(\dfrac{3}{4}\) times the length and the width of
Rectangle A. Rectangle C has a length and a width that
are both \(\dfrac{3}{4}\) times the length and the width of
Rectangle B. What is the perimeter, in inches, of
Rectangle C ?
The original perimeter of Rectange A is:
$$ P = 2l+2w $$
$$ P = 2(64)+2(48) $$
$$ P = 128+96 $$
$$ P = 224 $$
The scale factor from Rectangle A to B is \(\dfrac{3}{4}\). Therefore,
$$ P_B = \frac{3}{4}P_A $$
$$ P_B = \frac{3}{4}(224) $$
$$ P_B = 168 $$
The same relationship holds from B to C.
$$ P_C = \frac{3}{4}P_B $$
$$ P_C = \frac{3}{4}(168) $$
$$ P_C = \boxed{126} $$