Question

raheem is considering two different layouts for a new garden. he needs to put a length of fence around whichever layout he chooses. which layout needs more fencing

Answer 1

We have to find the length of the circumference and the perimeter of the rectangle.

The circumference is defined by

$C=\pi d$

According to the graph, the diameter is 12 units long.

$C=3.14\cdot12=37.68$

Hence, there are needed 37.68 units to put a fence on the circumference.

On the other hand, we have to find the width and length of the rectangle with the distance formula.

$d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}$

For the base, we use the points (-2, -10) and (10, -1)

$\begin{gathered} d=\sqrt[]{(10-(-2))^2+(-1-(-10))^2} \\ d=\sqrt[]{(10+2)^2+(-1+10)^2} \\ d=\sqrt[]{12^2+9^2}=\sqrt[]{144+81}=\sqrt[]{225} \\ d=15 \end{gathered}$

The base of the rectangle is 15 units long.

For the height, we use the points (-2, -10) and (-5, -6).

$\begin{gathered} d=\sqrt[]{(-5-(-2))^2+(-6-(-10))^2} \\ d=\sqrt[]{(-5+2)^2+(-6+10)^2} \\ d=\sqrt[]{(-3)^2+4^2}=\sqrt[]{9+16}=\sqrt[]{25} \\ d=5 \end{gathered}$

The height of the rectangle is 5 units.

Then, we find the perimeter.

$P=2(w+l)=2(15+5)=2(20)=40$

The perimeter of the rectangle is 40 units.

Hence, there would be needed more fencing for the rectangle than the circle.