The bisectors of angles A and B at the lateral side AB of the trapezoid ABCD intersect at point F. Find AB if AF = 16 BF = 12.
| August 8, 2021 | education
By the property of the bisectors drawn from the vertices of the lateral side, the bisectors intersect at right angles, therefore, the triangle ABF is rectangular with right angles at the vertices of F.
From the right-angled triangle ABF, by the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = AF ^ 2 + BF ^ 2 = 16 ^ 2 + 12 ^ 2 = 256 + 144 = 400.
AB = 20 cm.
Answer: The AB side of the trapezoid is 20 cm.
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