A rectangle is inscribed in a circle with a radius of 65, one side of which is 2.4 times larger than the other. Find the area of a rectangle.

univerkov | January 19, 2021 | education

The diagonal of a rectangle inscribed in a circle is the diameter of the circle, and the current O divides the diagonal in half, then ВD = 2 * R = 2 * ВO = 2 * 65 = 130 cm.

The AВD triangle is rectangular, then ВD ^ 2 = AB ^ 2 + AD ^ 2.

Let the side length AB = X cm, then, by condition, AD = 2.4 * X cm.

1302 = X ^ 2 + (2.4 * X) ^ 2.

6.76 * X ^ 2 = 16900.

X ^ 2 = 16900 / 6.76 = 2500.

X = AB = 50 cm.

AD = 2.4 * 50 = 120 cm.

Determine the area of the rectangle.

Savsd = AВ * AD = 50 * 120 = 6000 cm2.

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