In an isosceles triangle with a side of 7cm, the median to the side is 5.5cm.

In an isosceles triangle with a side of 7cm, the median to the side is 5.5cm. Find the length of the base of the triangle.

As we know from the school geometry course, any median in a triangle can be calculated, thanks to the following formula:

Ma = 1/2 * √ (2b ^ 2 + 2c ^ 2 – a ^ 2), where Ma is the median that is drawn to side a.

Let us determine what the base of the triangle will equal if from the condition of our problem we know for sure that the median that is drawn to the side equal to 7 cm is 5.5 centimeters:

5.5 = 1/2 * √ (2 * 7 ^ 2 + 2c ^ 2 – 7 ^ 2);

5.5 = 1/2 * √ (49 + 2c ^ 2);

121 = 49 + 2c ^ 2;

c ^ 2 = 36;

c1 = 6;

c2 = -6 (not suitable).

Answer: 6 cm.