ABCD quadrilateral AB parallel to CD BC parallel to AD, the perimeter of triangle AOD is 25cm, AC is 16cm, BD is 14cm. find BC -?

| February 10, 2021 | education

1. О – the point of intersection of the diagonals of the quadrangle AC and ВD.

2. By the condition of the problem, the opposite sides AB and СD, BC and AD of the quadrilateral AВСD are parallel. Therefore, this geometric figure is a parallelogram.

3. According to the properties of the parallelogram, the diagonals are divided by the intersection point into two identical lengths, that is, AO = CO = 16: 2 = 8 cm. ВO = DO = 14: 2 = 7 cm.

4. Calculate the length of the ABP side of the parallelogram using the formula for calculating the perimeter (P) triangle AOD:

R = AD + AO + DO.

AD + 8 + 7 = 25.

AD = 25 – 15 = 10 cm.

5. According to the properties of a parallelogram, the sides opposite each other are equal.

Therefore, BC = AD = 10 cm.

Answer: the length of the BC side of the AВСD parallelogram is 10 cm.



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