In parallelogram ABCD, a perpendicular pubescent from vertex B to side AD divides it in half.

| March 6, 2021 | education

In parallelogram ABCD, a perpendicular pubescent from vertex B to side AD divides it in half. Find the diagonal BD and the sides of the parallelogram if you know that the pyrimeter of the parallelogram is 3.8 m and the perimeter of triangle ABD is 3 m.

1. ВН – perpendicular.

2. Perimeter of triangle ABD:

AB + BD + AD = 3 cm.

3. The perimeter of the parallelogram ABCD:

2 (AB + AD) = 3.8 cm.

4. AB + AD = 1.9 cm. Substitute in the first expression:

1.9 + BD = 3 cm.

BD = 3 – 1.9 = 1.1 cm.

5. Triangles AВН and ВDH are equal on two sides and the angle between them (ВН = DH. ВН – common side. Angle ABН = angle BHD = 90 °).

Therefore, BD = AB = 1.1 cm.

6. Calculate the length AD:

AD = 1.9 – AB = 1.9 – 1.1 = 0.8 cm.

7. AD = BC = 0.8 cm. AB = CD = 1.1 cm. BD = 1.1 cm.



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