On the side BC of rectangle ABCD, in which AB = 56 and AD = 89, point E is marked

On the side BC of rectangle ABCD, in which AB = 56 and AD = 89, point E is marked so that the angle EAB = 45 degrees. find ED.

Point E divides segment BC into segments BE and EC. The angle EAB is 45 °, which means that in triangle ABE the angle BEA will also be 45 °, the triangle will be isosceles and sides AB and BE will be 56.

Let’s calculate the segment EC.

EC = BC – BE;

EC = 89 – 56 = 33.

The triangle ECD is rectangular and by the Pythagorean theorem we find the side ED.

ED² = EC² + CD²;

ED² = 33² + 56²;

ED² = 4225;

ED = √4225 = 65.

Answer: ED is 65.