The length of one side of the parallelogram is 4 cm longer than the other. Calculate the perimeter of the parallelogram

| May 10, 2021 | education

The length of one side of the parallelogram is 4 cm longer than the other. Calculate the perimeter of the parallelogram if one of its diagonals makes an angle of 30 and 45 degrees with the sides of the parallelogram.

Since ABCD is a parallelogram, then AD is parallel to BC, and then the angle CAD = ACB = 30 as criss-crossing angles at the intersection of parallel lines AD and BC secant AC.

Let the side length AB = X cm, then BC = X + 4 cm.

By the theorem of sines, in the triangle ABC.

ВС / Sin45 = AB / Sin30.

X * Sin45 = (X + 4) * Sin30.

X * (√2 / 2) = (X + 2) * 1/2.

X * √2 = X + 4.

X = AB = 4 / (√2 – 1) = 4 * (√2 + 1) / 1 = 4 * (√2 + 1) = 4 + 4 * √2 cm.

BC = 4 + 4 * (√2 + 1) = 8 + 4 * √2 cm.

Ravsd = 2 * (8 + 4 * √2 + 4 + 4 * √2) = 24 + 16 * √2 cm.

Answer: The perimeter of the parallelogram is 24 + 16 * √2 cm.



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