In trapezoid ABCD, the diagonal AC is perpendicular to the side of CD and is the bisector of angle A.

| April 21, 2021 | education

In trapezoid ABCD, the diagonal AC is perpendicular to the side of CD and is the bisector of angle A. Find the length AB, if the perimeter of the trapezoid is 35 cm, angle D = 60 degrees.

In a right-angled triangle ACD, we calculate the value of the angle CAD. Angle CAD = 190 – 90 – 60 = 30. Since the angle against the leg CD is 30, then CD = AD / 2. AD = 2 * CD.

By condition, AC is the bisector of angle A, then the angle BAD = CAD * 2 = 30 * 2 = 60.

Since the angle BAD = CDA, the trapezoid is isosceles, AB = CD.

The bisector AC cuts off the isosceles triangle ABC from the trapezium, to which, AB = BC.

Then AB = BC = CD, and AD = 2 * AB.

Let the length AB = X cm, then Ravsd = AB + BC + CD + AD = X + X + X + 2 * X = 35 cm.

5 * X = 35.

X = AB = 35/5 = 7 cm.

Answer: The length of the AB side is 7 cm.



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