ABCD- rectangular trapezoid with bases AD-9cm and BC-4cm. Find the length of the diagonal AC if it is perpendicular to the side of the trapezoid
By condition, the diagonal AC is perpendicular to CD, and therefore the triangle ACD is rectangular.
In the ABC triangle, the BCA angle is equal to the CAD angle of the ACD triangle as criss-crossing angles, then the right-angled triangles ABC and CAD are similar in acute angle.
In similar triangles, AC / AD = BC / AC.
AC ^ 2 = AD * BC = 9 * 4 = 36.
AC = 6 cm.
Answer: The diagonal of the trapezoid is 6 cm.
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