SOLUTION: In the diagram below, AGCD is a rectangle and GF=FC. Find the length of FE in cm. Diagram: https://imgur.com/a/hzXoD2g

Algebra ->  Length-and-distance -> SOLUTION: In the diagram below, AGCD is a rectangle and GF=FC. Find the length of FE in cm. Diagram: https://imgur.com/a/hzXoD2g      Log On


   

Question 1149198: In the diagram below, AGCD is a rectangle and GF=FC. Find the length of FE in cm.
Diagram: https://imgur.com/a/hzXoD2g
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


There are undoubtedly many different paths to the solution; here is what I came up with.

AB = AD = 4, so extend DC to H so that ABHD is a square. Extend AF to H, completing diagonal AH of the square. Note triangle FCH is a 45-45-90 right triangle.

Triangles ABE and HCE are similar; because CH = 2 and AB = 4, the ratio of similarity is 1:2. Then

EH%2FEA+=+1%2F2
EH%2FAH+=+1%2F3
AH+=+4%2Asqrt%282%29
EH+=+%281%2F3%29AH+=+%284%2F3%29%2Asqrt%282%29
FH+=+2%2Asqrt%282%29
EF+=+FH-EH+=+%282%2F3%29%2Asqrt%282%29