The middle line of the trapezoid is 50 cm. The smaller base is 35 cm. Find the larger base.

Given:
trapezoid ABCE,
OH – middle line,
ВС and АЕ – trapezoid bases,
BC = 35 centimeters,
OH = 50 centimeters.
Find the length of the base AE -?
Solution:
Consider the trapezoid ABCE.
The middle line of a trapezoid is equal to the half-sum of its bases, that is:
OH = 1/2 * (BC + AE);
2 * OH = BC + AE;
AE = 2 * OH – BC;
AE = 2 * 50 – 35;
AE = 100 – 35;
AE = 65 centimeters.
Answer: the length of the larger base is 65 centimeters.