For the rectangle abcd with sides ab = 16 and bc = 6, the condition de = ce is satisfied. Find P and S of triangle ABE.

Since the figure is a rectangle, then CD = AB = 16 cm, AD = BC = 6 cm.

By condition, DE = CE, then DE = CE = CD / 2 = 16/2 = 8 cm.

In a right-angled triangle ADE, by the Pythagorean theorem, we determine the length of the hypotenuse AE.

AE ^ 2 = AD ^ 2 + DE ^ 2 = 6 ^ 2 * 8 ^ 2 = 36 + 64 = 100.

AE = 10 cm.

Since the triangles ADE and BCD are equal on two sides, then BE = AE = 10 cm.

Then the perimeter of the triangle ABE = 2 * AE + AB = 2 * 10 + 16 = 36 cm.

In triangle ABC, the height will be the side of the AD of the rectangle, then Save = AB * AD / 2 = 16 * 6/2 = 48 cm2.

Answer: The perimeter of triangle ABE is 36 cm, the area is 48 cm.