The diagonals of the rhombus form angles with its side, one of which is half the other

| September 7, 2021 | education

The diagonals of the rhombus form angles with its side, one of which is half the other, calculate the length of the smaller dioganal of the rhombus if its perimeter is 16cm.

In a rhombus, the lengths of all its sides are equal.

Determine the length of the rhombus side.

AB = BC = CD = AD = P / 4 = 16/4 = 4 cm.

Let the value of the angle BAO = X0, then, by condition, the angle ABO = 2 * X0.

The diagonals of the rhombus intersect at an angle of 90, the angle AOB = 90.

The sum of the catch of the triangle is 180, then 180 = 90 + X + 2 * X.

3 * X = 90.

X = 30.BAO angle = 30.

Leg BO lies opposite angle 30, and therefore is equal to half of the hypotenuse AB.

BО = AB / 2 = 4/2 = 2 cm.

Then the smaller diagonal BD = BO * 2 = 2 * 2 = 4 cm.

Answer: The length of the smaller diagonal is 4 cm.



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