In parallelogram ABCD, the obtuse bisector DE divides the opposite side in a ratio of 1: 2.

| June 23, 2021 | education

In parallelogram ABCD, the obtuse bisector DE divides the opposite side in a ratio of 1: 2. What is the perimeter of parallelogram ABCD if side length AB is 10 cm?

Since BE is the bisector of the angle, the angle ABE = CBE. The angle CBE =  AEB as criss-crossing angles at the intersection of parallel lines AD and BC secant BE, therefore, triangle ABE is isosceles, AE = AB 10 cm.

Let the length of the segment DE = X cm, then, by condition, the length of the segment AE = 2 * X cm.

Then, since AB = AE = 10 cm, then 2 * X = 10 cm. X = 10/2 = 5 cm.

DE = 5 cm, AE = 10 cm, then AD = 10 + 5 = 15 cm.

Let’s define the perimeter of the rectangle. Ravsd = 2 * (AB + AD) = 2 * (10 + 15) = 50 cm.

A variant is possible, if AE = X cm, then DE = 2 * X cm.

Then AE = X = 10 cm, and DE = 2 * X = 20 cm. AD ​​= 10 + 20 = 30 cm.

Then Ravsd = 2 * (AB + AD) = 2 * (10 + 30) = 80 cm.

Answer: The perimeter of a parallelogram is 50 cm or 80 cm.



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