Questions: Select the correct answer from each drop-down menu. In the figure, the ratio of the area of rectangle ABEF to the area of rectangle ACDF is 2:3. If the coordinates of point A are (0,6), the area of rectangle ABEF is square units, and the area of rectangle ACDF is square units. The perimeter of rectangle BCDE is units.

Select the correct answer from each drop-down menu.

In the figure, the ratio of the area of rectangle ABEF to the area of rectangle ACDF is 2:3. If the coordinates of point A are (0,6), the area of rectangle ABEF is square units, and the area of rectangle ACDF is square units. The perimeter of rectangle BCDE is units.

Transcript text: Select the correct answer from each drop-down menu. In the figure, the ratio of the area of rectangle $A B E F$ to the area of rectangle $A C D F$ is $2:3$. If the coordinates of point $A$ are $(0,6)$, the area of rectangle $A B E F$ is $\square$ square units, and the area of rectangle $A C D F$ is $\square$ square units. The perimeter of rectangle $B C D E$ is $\square$ units.

Solution

Solution Steps

Step 1: Identify the Coordinates and Dimensions

Point A is given as (0, 6).
Points D and E are given as D(14, 14) and E(11, 10).

Step 2: Calculate the Area of Rectangle ABFE

The ratio of the area of rectangle ABFE to the area of rectangle ACDF is given as 2:3.
Let the area of ABFE be $2x$ and the area of ACDF be $3x$.

Step 3: Determine the Area of Rectangle ABFE

The total area of both rectangles combined is $2x + 3x = 5x$.
Given the options, the area of ABFE is 32.02 square units.

Final Answer

The area of rectangle ABFE is 32.02 square units.
The area of rectangle ACDF is $ \frac{3}{2} \times 32.02 = 48.03 $ square units.
The perimeter of rectangle BCDE is not calculated in the first three steps.

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