In an isosceles trapezoid, ABCD, ab and cd are equal, CH is the height drawn to the greater base of AD.

In an isosceles trapezoid, ABCD, ab and cd are equal, CH is the height drawn to the greater base of AD. Find the length of the segment HD if the middle line KM is 12 and the base is less than 4.

In order to calculate the length of the segment НD, it is necessary to find the length of the larger base AD.

Since the middle line of a trapezoid is half the sum of its bases:

m = (ВС + АD) / 2, then:

BC + AD = 2m;

AD = 2m – BC;

AD = 2 12 – 4 = 24 – 4 = 20 cm.

Since the smaller base is equal to the segment KН located between two heights, and the segments AK and HD are equal, since this trapezoid is isosceles, then:

AK = HD = (AD – BC) / 2;

AK = HD = (20 – 4) / 2 = 16/2 = 8 cm.

Answer: the length of the segment НD is 8 cm.