In an isosceles triangle ABC with base AC, a median AD of 13 cm is drawn to the lateral side.
| February 20, 2021 | education
In an isosceles triangle ABC with base AC, a median AD of 13 cm is drawn to the lateral side. Find the sides of triangle ABC if the perimeters of triangles ABD and ADC are 49 cm and 30 cm, respectively.
The perimeter of the AВD triangle is: Ravd = AB + ВD + AD = 49 cm.
Then (AB + ВD) = 49 – AD = 49 – 13 = 36 cm.
The perimeter of the AСD triangle is: Rasd = AС + СD + AD = 30 cm.
Then (AC + СD) = 30 – AD = 30 – 13 = 17 cm.
Since AD is the median of the triangle, then ВD = СD, and ВС= ВD + СD).
Then: (AB + ВD) + (AC + СD) = 36 + 17 = 53 cm.
AB + AC + ВD = Ravs = 53 cm.
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