## 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. More Details

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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

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