Wednesday, February 22, 2023

Geometry Problem 1510: Congruence of Triangles, Perimeter, Measurement. Difficulty Level: High School.

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.

Geometry Problem 1510: Congruence of Triangles, Perimeter, Measurement. Difficulty Level: High School.

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2 comments:

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

    Then 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

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

    Let 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

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