If you're not a fan of the distance formula, there's another way to do this. See the lenghts of FE and DE as the hypoteneuses of special right triangles. From F horizontally to the right and from E vertically downward can be measured where the lines meet at a right angle. Their lengths are 6 and 8 respectively or 2 times the 3-4-5 special right triangle lengths. So that makes FE 2 times 5 or 10. Doing the same for DE gives us 5. Since area of a rectangle is base times height, we can see that the heights for ABEF and ACDF are the same and can be expressed as X. We can set up a ratio of the areas as 10X/15X, cancel the Xs and simplify the fraction to be 2/3 or a ratio of 2:3. The area of ABEF needs a specific height (rather than X) to go with its base of 10. We know that AF is the hypoteneus of a right triangle with vertical side 4 and horizontal side 5. Using the Pythagorean Theorem we can find AF and multiply it by 10 to get . . .? We can use the length of AF and 10+5 to get the area of ACDF. The perimeter of BCDE is 2 times AF plus 2 times 5.

Sarah L.

asked • 02/19/21# 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 __2:1, 2:3, 3:4, or 3:5__.

If the coordinates of point *A* are (0,6), the area of rectangle *ABEF* is __32.02, 48.03, 64.03, or 96.05__ square units, and the area of rectangle *ACDF* is __48.03, 64.03, 96.05, or 128.07__ square units.

The perimeter of rectangle *BCDE* is __20.61, 22.81, 25.61, or 32.81__ units.

*Please select one of the underlined for each section*

## 2 Answers By Expert Tutors

Use distance formula to find the length of AF (sqr root of 41) and FE (10 units) Find area of rectangle.

Area of ABEF 64.03

similarly find the length of DF (15 units) using distance formula.

Area of ACDF 96.05

difference between the lengths will give you length of DE as 5 units.

perimeter is 22.81

find ratio of the areas 64.03/96.05 = 0.666667 = 2/3

hope this helps!

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