Answer
(a) Perimeter = $30~feet$, Area= $54~feet^2$
(b) Perimeter multiplied by 3. Area multiplied by 9.
(c) Perimeter multiplied by 4. Area multiplied by 16.
Work Step by Step
(a)
We know the the dimensions are now tripled:
length: $3*3=9$ feet
width: $2*3=6$ feet
(See sketch.)
New perimeter:
$9*2+6*2=18+12=30$ feet
New area:
$9*6=54~feet^2$
(b)
We see that the perimeter has tripled:
$\displaystyle \frac{new~perimeter}{old~perimeter}=\frac{30}{10}=3$
We see that the area is 9 times the original area:
$\displaystyle \frac{new~area}{old~area}=\frac{54}{6}=9$
(c)
If the length and width were multiplied by $4$, we would expect the perimeter to multiply by $4$ and the area to multiply by $16$. This is because the perimeter multiplies by the same factor that the lengths do and the area multiplies by that factor squared ($4^2=16$). This is a general rule of geometry.
