The height dropped from the top of an obtuse angle of an isosceles trapezoid divides the base into two segments

| August 17, 2021 | education

The height dropped from the top of an obtuse angle of an isosceles trapezoid divides the base into two segments, the lengths of which are 6 and 30 cm. What are the bases of the trapezoid?

Consider an isosceles trapezoid ABCD, where the sides are AB = CD and the bases are AD and BC.

We drop the heights BM and CN of the trapezoid from the vertices B and C. Obviously, BM = CN and BC = MN.

By the condition of the problem, we have that AM = 6 cm and MD = 30 cm.

Consider triangles ABM and CDN. Both triangles are rectangular, in which the hypotenuse AB = CD and the legs BM = CN are equal.

Therefore, triangles ABM and CDN are equal. Hence, AM = ND.

Thus, we get:

BC = MN = MD – ND = MD – AM = 30 – 6 = 24 cm,

AD = AM + MD = 6 + 30 = 36 cm.

Answer: the bases of the trapezoid are 24 cm and 36 cm.



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