Find the smaller base of the isosceles trapezoid if the height drawn from the top of the obtuse angle divides the larger

Find the smaller base of the isosceles trapezoid if the height drawn from the top of the obtuse angle divides the larger base into 4-inch and 16-inch segments.

ABCD – isosceles trapezoid: AB = CD, AD – larger base, BC – smaller base, BH – height, AH = 4 dm, DH = 16 dm.
It is known from the properties of an isosceles trapezoid that the height of an isosceles trapezoid drawn from the top of an obtuse angle divides the base into two segments, one of which is equal to the half-sum of the bases, and the second to the half-difference of the bases.
In this way:
AH = (AD – BC) / 2;
DH = (AD + BC) / 2.
The larger base AD consists of segments:
AD = AH + DH;
AD = 4 + 16 = 20 (dm).
Substitute the known values ​​and find the length of the smaller base of the BC:
(20 – BC) / 2 = 4;
(20 + BC) / 2 = 16.
By proportion:
20 – BC = 8 ⇒ – BC = 8 – 20 ⇒ – BC = – 12 ⇒ BC = 12 (dm);
20 + BC = 32 ⇒ BC = 32 – 20 ⇒ BC = 12 (dm).
Answer: BC = 12 dm.