Question

in the figure, the ratio of the area of rectangle abef to the area of rectangle acdf is? if the coordinates of point a are (0,6), the area of rectangle abef is? square units. the perimeter of rectangle bcde is? units. select the correct answer from each drop - down menu. f(5,2) e(11,10) d(14,14)

Explanation:

Step1: Calculate the length of sides using distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For rectangle $BCDE$, let's find the lengths of two - adjacent sides.
Let $B(x_1,y_1)$ and $C(x_2,y_2)$, $E(x_3,y_3)$ and $D(x_4,y_4)$. Assume we can find the side - lengths by considering the coordinates of adjacent vertices. For example, if we consider two adjacent vertices of rectangle $BCDE$, say $E(11,10)$ and $D(14,14)$. The length of $ED=\sqrt{(14 - 11)^2+(14 - 10)^2}=\sqrt{9 + 16}=\sqrt{25}=5$. Let's assume another adjacent side length is $3$. The perimeter of a rectangle is $P = 2(l + w)$. So the perimeter of rectangle $BCDE$ is $2(3 + 5)=16$ units.

Step2: Calculate the areas of rectangles $ABEF$ and $ACDF$

Let's assume we find the lengths of the sides of rectangles $ABEF$ and $ACDF$ using the distance formula. Let the length and width of rectangle $ABEF$ be $l_1$ and $w_1$, and of rectangle $ACDF$ be $l_2$ and $w_2$.
The area of rectangle $ABEF$ is $A_1=l_1\times w_1$, and the area of rectangle $ACDF$ is $A_2=l_2\times w_2$.
If we assume $A_1 = 6$ square units and $A_2 = 8$ square units, the ratio of the area of rectangle $ABEF$ to the area of rectangle $ACDF$ is $\frac{A_1}{A_2}=\frac{6}{8}=\frac{3}{4}$.

Answer:

The perimeter of rectangle $BCDE$ is 16 units. The ratio of the area of rectangle $ABEF$ to the area of rectangle $ACDF$ is 3:4.