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In rectangle ABCD, AB = 3 and BC = 9. The rectangle is folded so that points A and

C coincide, forming the pentagon ABEFD. What is the length of segment EF? Express
your answer in simplest radical form.

2 Answers

3 votes

Answer:

Explanation:

To find the length of segment EF in pentagon ABEFD, we need to determine the distance between points E and F after the rectangle ABCD is folded.

Since AB = 3 and BC = 9, the length of the rectangle's diagonal, AC, can be found using the Pythagorean theorem. Let's denote the length of segment AC as x:

AC^2 = AB^2 + BC^2

x^2 = 3^2 + 9^2

x^2 = 9 + 81

x^2 = 90

x = sqrt(90)

x = 3sqrt(10)

When the rectangle is folded, points A and C coincide, meaning that the length of segment EF is equal to x.

Therefore, the length of segment EF in pentagon ABEFD is 3sqrt(10), expressed in simplest radical form.

User Zephinzer
by
6.6k points
2 votes

The length of segment EF in pentagon ABEFD is 12.


Given:

Rectangle ABCD with AB = 3 and BC = 9

Folding the rectangle along AC to form pentagon ABEFD

Objective:

Determine the length of EF in pentagon ABEFD, in simplest radical form.

Solution:

Visualize the fold: Imagine folding rectangle ABCD along diagonal AC until points A and C coincide. This creates pentagon ABEFD with EF perpendicular to AD.

Identify similar triangles: Notice triangles ACB and AEF are similar due to sharing two corresponding angles (right angles and angle CAB).

Set up proportions: Use the ratio of corresponding sides in the similar triangles:

AC / EF = AB / CB

Substitute known values:

(AB + BC) / EF = AB / CB

(3 + 9) / EF = 3 / 9

12 / EF = 1/3

Solve for EF:

EF = 12 * 3

EF = 36 / 3

EF = 12

Final Answer:

The length of segment EF in pentagon ABEFD is 12.



The probable question is in the image attached.

In rectangle ABCD, AB = 3 and BC = 9. The rectangle is folded so that points A and-example-1
User George John
by
7.7k points