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.