In a convex quadrilateral ABCD, the diagonals are halved by the intersection point.

| August 9, 2021 | education

In a convex quadrilateral ABCD, the diagonals are halved by the intersection point. Find the perimeter of this quad if the sum of the adjacent sides is 13.6.

Let us prove that triangle AOD is equal to triangle BOC.

The angle AOD is equal to the angle BOC as the vertical angles at the intersection of straight lines AC and BD.

AO = OC, BO = OD by condition, as half of the diagonals. Then the triangle AOD is equal to the triangle BOC on two sides and the angle between them.

Then AD = BC.

Similarly, the equality of triangles AOB and COD is proved, and therefore AB = CD.

By condition, the sum of adjacent sides is 13.6 cm.Let AB + BC = 13.6 cm, and since AB = CD, and BC = AD, then AD + CD = 13.6 cm.

The perimeter of the quadrilateral is: P = (AB + BC) + (CD + AD) = 13.6 + 13.6 = 27.2 cm.

Answer: The perimeter of the quadrangle is 27.2 cm.



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