Geometry Problem 1514. Post your solution in the comment box below.

Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

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To post a solution to this problem click Comment underneath the post, or click into the line that says, “Enter Comment.” Type what you want to say and press Publish to post your solution.

To post a solution to this problem click Comment underneath the post, or click into the line that says, “Enter Comment.” Type what you want to say and press Publish to post your solution.

GK = 6V2 ( square root) It will be explained in the sketch.

ReplyDeleteIn Tr. GKH, < GKH > 90 so GH > GK and so GK < 6 but you say GK = 6.sqrt.2 > 6. Hence the answer is incorrect

Deletehttps://photos.app.goo.gl/4AzheNU5tkxHPCtt8

DeleteThis and some of previous are for beginners (students) : https://photos.app.goo.gl/upPuhDvxkQ8sj54B8

DeleteSince < AFE = 120 and < MFE = 90, <AFM = 30.

ReplyDeleteSo <GFM = < GFA - < AFM = 45 - 30 =15 and < GFK = < NFM - < GFM = 45 - 15 = 30.

Hence Tr. GFK is 30-60-90 and so

GK = GF/2 = (6.sqrt.2)/2 which is the same as 6 / sqrt.2

Sumith Peiris

Moratuwa

Sri Lanka

Some interesting results

ReplyDelete1) Tr.s ABG, AFM, FHE, END, GHM, MHN are all congruent and isosceles 75-30-75

2) B,G,K are collinear

3) Tr.s FEN & BKF are right isosceles

Not for post, just take a look, if square ASTB is added, then P, M, S are interesting points. https://photos.app.goo.gl/8xKYnMSYxAXuR9Jw7

ReplyDelete