In trapezoid ABCD, the sides AB and CD are equal, CH is the height drawn to the larger base AD.

In trapezoid ABCD, the sides AB and CD are equal, CH is the height drawn to the larger base AD. Find the bottom of the segment DH if the midline MN of the trapezoid is 12 and the smaller base BC is 7.

Apply the formula for the midline of a trapezoid and determine the length of the larger base.

MН = (BC + AD) / 2.

AD = 2 * MН – BC = 2 * 12 – 7 = 17 cm.

Let’s draw the second height of the ВK.

Quadrilateral ВСНK is a rectangle, then KН = BC = 7 cm.

Since, by condition, AB = CD, the trapezoid is isosceles, then the triangles ABK and CDH are equal in hypotenuse and acute angle, and therefore AK = DH.

Then AK = DH = (AD – BC) / 2 = (17 – 7) / 2 = 10/2 = 5 cm.

Answer: The length of the segment DH is 5 cm.