Find the perimeter of rectangle ABCD if AB = 10cm, angle BAO = 30 °, and diagonal AC = 16cm.

| September 17, 2021 | education

Given: ABCD – rectangle; AB = 10 cm; angle VAO = 30 °; AC – diagonal = 16 cm.

Find: Рabcd -?.

Let’s carry out dangoli AC and BD. Let the point O be the intersection point of these diagonals, therefore, the midpoint of these diagonals.

Angle BAO = angle DCO – as intersecting angles with parallel straight lines BC and AD (by the definition of a rectangle: opposite sides are equal and parallel) and secant AC.

Or:

Angle BAD = 90 ° – by the definition of a rectangle. Therefore, the angle OAD = 90 ° – 30 ° = 60 °. In triangle ACD: angle ACD = 180 ° – (90 ° + 60 °) = 30 °.

The leg lying opposite an angle of 30 ° is equal to half the hypotenuse. Hence, AD = 1/2 AC = 1/2 * 16 = 16/2 = 8 (centimeters).

BC = AD = 8 – by the definition of a rectangle.

P = 2 * (a + b) = 2 * (10 + 8) = 2 * 18 = 36 (centimeters).

Answer: P = 36 centimeters.



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