A perpendicular drawn from the intersection of the diagonals of the rhombus to its side divides it into segments

| March 16, 2021 | education

A perpendicular drawn from the intersection of the diagonals of the rhombus to its side divides it into segments, the difference between which is 7 cm.Find the perimeter of the rhombus if its height is 24 cm.

Let us determine the length of the OH segment, which is equal to half the length of the CК height. OH = 24/2 = 12 cm.

The diagonals of the rhombus at the point of their intersection are halved and intersect at right angles. Then AO = OS = AC / 2, OB = OD = BD / 2, and triangle AOD is rectangular.

Let the length of the segment DH = X cm, then AH = (X + 7) cm.

The height of OH is drawn from the top of the right angle to the hypotenuse, then OH ^ 2 = AH * DH = (X + 7) * X = 144.

X ^ 2 + 7 * X – 144 = 0.

Let’s solve the quadratic equation.

X1 = -16. (Doesn’t fit because <0).

X2 = 9.

DН = 9 cm.

AH = 9 + 7 = 16 cm.

AD = 9 + 16 = 25 cm.

Ravsd = AD * 4 = 25 * 4 = 100 cm.

Answer: The perimeter of the rhombus is 100 cm.



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