In a parallelogram with a height of 2, the root of 2 cm, one of the corners is 5 times larger than the other, then

| April 10, 2021 | education

In a parallelogram with a height of 2, the root of 2 cm, one of the corners is 5 times larger than the other, then … A) one side is 4 cm C) one side is shorter and the other is longer by the root of 2 cm C) both sides are shorter than the height by the root of 2 cm E) the side is shorter than the height E) one side is equal to 4 root of 2 cm

Let ABCD be a given parallelogram, HH – height. BH = 2√2 cm.

The opposite angles of the parallelogram are equal, which means that the angle A in the angle B is 1 to 5, let the angle A = x, then the angle B = 5x.

In a parallelogram, two sides adjacent to one side add up to 180 °:

x + 5x = 180 °,

6x = 180 °,

x = 30 ° (angle A),

5x = 150 ° (angle B).

Consider a triangle ABN (angle H = 90 °): angle A = 30 °. In a right-angled triangle opposite an angle of 30 ° lies a leg, half the size of the hypotenuse. Hence, AB = 4√2 cm.

A) One side is 4 cm. We only know the length of the side AB (and the opposite side CD). Wrong.

C) One side is shorter and the other is √2 cm longer. We do not know the second side of the parallelogram. Wrong.

C) Both sides are shorter than the height by √2 cm. Side AB is shorter than the height by 2√2. Wrong.

E) One side is 4√2 cm. Yes, that’s right, AB = CD = 4√2 cm.



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