# One diagonal of the rhombus is 2 cm larger than the other. If the area of this rhombus is 12 cm2, then what is its large diagonal?

January 20, 2021 | education

| Let the length of the larger diagonal be AC = X cm, then the length of the smaller diagonal, by condition, is equal to ВD = (X – 2) cm.

The area of the rhombus through its diagonals is equal to: Savsd = AC * ВD / 2 = X * (X – 2) / 2.

12 * 2 = X ^ 2 – 2 * X.

X ^ 2 – 2 * X – 24 = 0.

Let’s solve the quadratic equation.

D = b2 – 4 * a * c = (-2) ^ 2 – 4 * 1 * (-24) = 4 + 96 = 100.

X1 = (2 – √100) / (2 * 1) = (2 – 10) / 2 = -8 / 2 = -4. (Doesn’t fit because <0).

X2 = (2 + √100) / (2 * 1) = (2 + 10) / 2 = 12/2 = 6.

AC = 6 cm.

Answer: The length of the larger diagonal is 6 cm.

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