Geometry Problem 1510. 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.

Let AB = c, BC = a and AC = b

ReplyDeleteThen CD = a = b - 14.......(1)

Also DF = c = b - 24........(2)

We are given that a + b + c = 124 .......(3)

(1) + (2) + b we get a + b + c = 3b - 38 = 124 from (3)

So 3b = 162 and b = 54

From (2) AB = c = b - 24 = 54 - 24 = 30

Sumith Peiris

Moratuwa

Sri Lanka

https://photos.app.goo.gl/NMEUvbczc1FiduxB7

ReplyDeleteLet a, b, c are 3 sides of triangle ABC

Per sketch attached we have

b-a= 14 ….(1)

b-c=24…(2)

a+b+c= 124 ….(3)

From (1) and (2) we have b= c+24 and a=c+10

Replace it in (3) we have c= 30, a=40 and b=54

So AB= c= 30