The bases of the rectangular trapezoid are 6 and 8, and the height is 5.

| May 26, 2021 | education

The bases of the rectangular trapezoid are 6 and 8, and the height is 5. Find the length of the line that connects the middle of the larger base to the middle of the larger side.

Let’s draw the diagonal of the AC trapezoid. In the formed right-angled triangle ABC, leg BC = 6 cm, leg AB = 5 cm, and by the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 5 ^ 2 + 6 ^ 2 = 25 + 36 = 61.

AC = √61 cm.

Consider triangle ACD. Point K, by condition, is the middle of the AD side, and the M point is the middle of the CD side, then the KM segment is the middle line of the ACD triangle.

The midline of a triangle is half the length of the side to which it is parallel.

KM = AC / 2 = √62 / 2 cm.

Or, triangle ACD is similar to triangle KMD in two angles, then:

KM / AC = KD / AD.

KM = AC * KD / AD = √61 * 4/8 = √61 / 2 cm.

Answer: KM = √61 / 2 cm.



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