One diagonal of the rhombus is 25cm longer than the other. The area of the rhombus is 50% larger than

| April 24, 2021 | education

One diagonal of the rhombus is 25cm longer than the other. The area of the rhombus is 50% larger than the area of the triangle, the base of which is 40cm, and the height is equal to the smaller diagonal of the rhombus. Find the diagonals of the rhombus.

Let the diagonal AC = X cm, then BD = 25 + AC cm.

The area of a rhombus is half the product of its diagonal. Sromba = AC * BD / 2 = AC * (25 + AC) / 2.

Since the height of the triangle is equal to the smaller diagonal of the rhombus, we also denote it as AC.

Then the area of the triangle is Str = KM * AC / 2 = 40 * AC / 2 = 20 * AC.

According to the condition Sromba = Str + 0.5 * Str = 1.5 * Str.

AC * (25 + AC) / 2 = 1.5 * 20 * AC.

25 * AC + AC2 = 60 * AC.

AC ^ 2 – 35 AC = 0.

AC * (AC – 35) = 0.

X1 = 0. (Doesn’t fit, since it doesn’t make sense).

X2 = 35 cm.

AC = 35 cm.

ВD = 35 + 25 = 60 cm.

Answer: The diagonals of the rhombus are 35 cm, 60 cm.



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