In an isosceles trapezoid, the height divides the larger base into segments equal to 5 and 12 cm.

In an isosceles trapezoid, the height divides the larger base into segments equal to 5 and 12 cm. Find the midline of the trapezoid.

Let’s call this trapezoid ABCD, where BC, AD are the bases, draw two heights BK, CL, then the length of AK will be 5 cm, and the length of KD will be 12 cm, then the length of LD will be equal to the length of AK and will also be equal to 5 cm.
KL = KD – LD = 12 – 5 = 7 cm.
Since the length of KL is equal to the length of the smaller base, then the length of BC is also 7 cm, we can find the middle line of the trapezoid if BC = 7 cm, AD = 17 cm.
(BC + AD) / 2 = (7 + 17) / 2 = 12 cm.
Answer: the length of the middle line is 12 cm.