The base of an isosceles triangle is 8 cm. The median drawn to the lateral side splits the triangle into two triangles

| November 29, 2020 | education

The base of an isosceles triangle is 8 cm. The median drawn to the lateral side splits the triangle into two triangles so that the perimeter of one triangle is 2 cm larger than the perimeter of the other. Find the side of this triangle.

Let’s call the triangle ABC, draw the median AD and get two triangles: ABD and ADC.
There will be two options:
1) Suppose ABD is greater than ADC. Then ABD Perimeter = ADC Perimeter + 2cm
Perimeter ABD = AB + AD + BD
Perimeter ADC = AD + DC + AC
AD – general; BD = DC, since the median divides BC into equal segments BD = DC; then we can conclude that AB is 2 cm larger than AC.
AB = AC + 2
AB = 8 + 2 = 10 cm
2) The second option would be if the perimeter of triangle ADC is greater than ABD. Then we can conclude that AB = AC – 2
AB = 8 – 2 = 6 cm
Answer: 10 cm or 6 cm



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