The midline of the trapezoid is 19 and one of the bases is 7. Find the other base of the trapezoid.

Given:
ABCD – trapezoid,
КP – middle line of trapezoid ABCD,
ВС, АD – bases of trapezoid ABCD,
BC = 7,
КP = 19.
Find the length of the base AD -?
Solution:
Consider the trapezoid ABCD. The midline of any trapezoid is equal to the half-sum of its bases. Hence
KP = 1/2 * (BC + AD); (we substitute the number 7 instead of the BC, and the number 19 instead of the KP)
19 = 1/2 * (7 + AD); (multiply the right and left sides by the number 2)
19 * 2 = 1/2 * (7 + AD) * 2;
38 = 7 + AD;
AD = 38 – 7;
AD = 31.
Answer: base length AD = 31.