In the triangle ABC, AB = BC, AM is the median, AB + BM = 9, MC + AC = 7. Find the sides of a triangle
| April 4, 2021 | education
Since AM is the median of the triangle, then BM = CM.
AB + BM = 9 cm.
MС + AC = 7 cm.
Let’s add two equations.
AB + BM + MС + AC = 16.
AB = BC, BM + MС = BC, then:
AB + BC + AC = 2 * AB + AC = 16 cm.
AC = 7 – BC = 7 – (BC / 2) = 7 – (AB) / 2.
Then, 2 * AB + 7 – (AB / 2) = 16 cm.
3 * AB / 2 = 16 – 7 = 9 cm.
3 * AB = 18.
AB = 18/3 = 6 cm.
BC = AB = 6 cm.
MС = 6/2 = 3 cm.
AC = 7 – 3 = 4cm.
Answer: The sides of the triangle are 6 cm, 6 cm, 4 cm.
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