The bisector of angle B of rectangle ABCD divides its side into segments AO and OD so that AO = 2OD.

univerkov | April 8, 2021 | education

The bisector of angle B of rectangle ABCD divides its side into segments AO and OD so that AO = 2OD. Calculate the lengths of the sides of a rectangle if its perimeter is 28cm.

Let the length of the segment OD = X cm, then, by condition, the length of the segment AO = 2 * OD = 2 * X cm.

The bisector ВO cuts off at the lateral side AB a rectangular, isosceles triangle AOB, then AB = AO = 2 * X cm.

Side length AD = (AO + OD) = (2 * X + X) = 3 * X cm.

Then the perimeter of the rectangle ABCD is: Ravsd = 2 * (AB + AD) = 28 cm.

2 * (2 * X + 3 * X) = 28.

10 * X = 28.

X = 28/10 = 2.8 cm.

Then AB = 2 * 2.8 = 5.6 cm.

AD = 3 * 2.8 = 8.4 cm.

Answer: The lengths of the sides of the rectangle are 5.6 cm and 8.4 cm.

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