In an obtuse triangle, the degree measure of one of the acute angles is 45°, and the length of the shortest altitude is 5 inches. If the perimeter of this triangle is 30 + 5√2 inches, find in square inches the area of the triangle.

In an obtuse triangle, the degree measure of one of the acute angles is 45°, and the length of the shortest altitude is 5 inches. If the perimeter of this triangle is 30 + 5√2 inches, find in square inches the area of the triangle.