One side of the parallelogram ABCD is 20 cm larger than the other. From the top of the obtuse angle B

| August 13, 2021 | education

One side of the parallelogram ABCD is 20 cm larger than the other. From the top of the obtuse angle B, the heights BM and BT are drawn, the lengths of which are 5 cm and 10 cm, respectively. Find the lengths of the sides of the parallelogram.

1. The length of the AD side is 20 cm longer than the CD side (according to the problem statement).

That is, AD = (CD + 20) see.

2. The area (S) of a parallelogram can be calculated using two formulas:

S = СD х ВТ = 10СD cm².

S = AD x BM = 5AD cm².

3. 10 CD = 5AD. Substitute in this expression (CD + 20) instead of AD:

10 CD = 5 (CD + 20).

5СD = 100,

CD = 20 cm.

AD = 20 + 20 = 40 cm.

4. According to the properties of a parallelogram, its opposite sides are equal.

Therefore AB = CD = 20 cm, BC = AD = 40 cm.

Answer: the sides of the parallelogram are AB = CD = 20 cm, BC = AD = 40 cm.



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