In parallelogram ABCD, the bisector of angle B intersects side AD at point E so that AE = 12, ED = 5.

In parallelogram ABCD, the bisector of angle B intersects side AD at point E so that AE = 12, ED = 5. Find the perimeter of the parallelogram.

ВE is the bisector of angle B, which means angle ABE = angle EBC.

And the angle AEB and the angle EBC are internal crosswise lying at two parallel and secant, which means they are equal.

Consider triangle ABE.

Angle B = angle E, so this triangle is isosceles.

Side AE = side AB and is equal to 12 cm.Let’s find side AD: 12 + 5 = 17 cm.

Then we find the perimeter: 12 * 2 + 17 * 2 = 24 +34 = 58 cm.