In a rectangular trapezoid ABCD (AD is parallel to BC, angle A = 90 °) BD = 5√2, angle abd = angle cbd and bd is parallel

In a rectangular trapezoid ABCD (AD is parallel to BC, angle A = 90 °) BD = 5√2, angle abd = angle cbd and bd is parallel to cd. Find the perimeter of the trapezoid

Let’s draw the CE height.
Segment AE = BC = 36 cm.
CE = √ (AC ^ 2-AE ^ 2) = √ (3600-1296) = √2304 = 48 cm.
By the property of the height CE from the vertex of the right angle ACD:
ED / CE = CE / AE.
Hence ED = CE ^ 2 / AE = 2304/36 = 64 cm.
AD = 36 + 64 = 100 cm
Answer: 100 cm