In parallelogram ABCD, the height BK divides side AD into segments AK and KD.

univerkov | May 18, 2021 | education

In parallelogram ABCD, the height BK divides side AD into segments AK and KD. Find the perimeter of the parallelogram if BK = 8cm, DB = 10cm, AK = 15cm.

1. The side AB of the parallelogram is the hypotenuse in the right-angled triangle ABK.

Using the formula of the Pythagorean theorem, we calculate its length:

AB = √AK ^ 2 + BK ^ 2 = √15 ^ 2 + 8 ^ 2 = √289 = 17 cm.

2. Calculate the length of the segment KD:

KD = √BD ^ 2 – BK ^ 2 = √10 ^ 2 – 8 ^ 2 = √100 – 64 = √36 = 6 cm.

3. AD = AK + DK = 15 + 6 = 21 cm.

4. Opposite sides of parallelogram ABCD are equal. Therefore, AB = DC.

BC = AD.

5. The perimeter of the parallelogram ABCD = 2AB + 2BC = 17 x 2 + 21 x 2 = 76 cm.

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