In the isosceles tradition ABCD, the height CH is drawn. Point H divides the larger base AD

In the isosceles tradition ABCD, the height CH is drawn. Point H divides the larger base AD into a segment with lengths 12 and 7. Find the length of the smaller base.

1. AH = 12 centimeters, DH = 7 centimeters. CH height. BC is the lesser base. AD is a larger base.

2. In accordance with the properties of an isosceles trapezoid, the length of the largest of the segments into which the height of CH divides the base AD is calculated by the formula:

AH = (BC + AD) ^ 2.

3. Using this formula, we calculate the length of the smaller base of the trapezoid:

ВС = 2АН – АD. AD = AH + DH = 12 + 7 = 19 centimeters.

BC = 2 x 12 – 19 = 5 centimeters.

Answer: the length of the BC, the smaller base of a given trapezoid, is 5 centimeters.