In an isosceles triangle ABC with base AC, a median BM of 5 cm is drawn. Find the length

In an isosceles triangle ABC with base AC, a median BM of 5 cm is drawn.Find the length of the base if the lateral side is 8 cm.

In an isosceles triangle, the median drawn to the base is also its height. So BM = CM, triangles ABM and CBM are equal, angle M is a straight line.

1) Find the MC segment by the Pythagorean theorem:

In the BCM triangle, BC = 8 cm (hypotenuse), BM = 5 cm.

BC ^ 2 = BM ^ 2 + MC ^ 2;

8 ^ 2 = 5 ^ 2 + MC ^ 2;

MC ^ 2 = 8 ^ 2 – 5 ^ 2;

MC ^ 2 = 64 – 25;

MC = √49;

MC = 7 cm.

2) Find the side of the speaker:

AC = 2 × MC;

AC = 2 × 7;

AC = 14 cm.

The length of the speaker base is 14 cm.