Find the length of the midline of a trapezoid, the diagonals are mutually perpendicular to their lengths 10 and 20

| August 10, 2021 | education

From the vertex C of the trapezoid, draw a straight line parallel to the side BD of the trapezoid, until it intersects with the straight line AD at point H.

Then the triangle ACH is rectangular, with a right angle at point C. The quadrilateral BCHD is a parallelogram, since BC is parallel to DH, and BD is parallel to CH, then CH = 10 cm.

From the right-angled triangle АСН, according to the Pythagorean theorem, we determine the length of the hypotenuse АН.

AH ^ 2 = AC ^ 2 + CH ^ 2 = 400 + 100 = 500.

AH = 10 * √5 cm.

AH = AD + DH.

Since DH = BC, then AH = AD + BC, which is the sum of the bases.

Let’s define the middle line of the trapezoid.

КР = (АD + ВС) / 2 = 10 * √5 / 2 = 5 * √5 cm.

Answer: The length of the middle line of the trapezoid is 5 * √5 cm.



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