In a rectangular trapezoid, an acute angle of 45 degrees, the large side is exactly 16 roots out of 2

| September 18, 2021 | education

In a rectangular trapezoid, an acute angle of 45 degrees, the large side is exactly 16 roots out of 2, the smaller diagonal is 20 cm, find the perimeter.

Let’s draw the height of the CH trapezoid.

The right-angled triangle СDН is isosceles, since one of its acute angle is 45, then СН = DH.

From the right-angled triangle СDН, we determine the length of the leg СН and DН.

CD ^ 2 = CH ^ 2 + DH ^ 2 = 2 * CH ^ 2.

CH ^ 2 = CD ^ 2/2 = (16 * √2) 2/2 = 256.

CH = DN = 16 cm.

From a right-angled triangle ACD, AH ^ 2 = AC ^ 2 – CH ^ 2 = 400 – 256 = 144.

AH = 12 cm.

Since ABCD is a rectangle, then BC = AH = 12 cm, AB = CH = 16 cm.

The length of the segment АD = АН + DH = 12 + 16 = 28 cm.

Let’s define the perimeter of the trapezoid.

Ravsd = AB + BC + CD + AD = 16 + 12 + 16 * √2 + 28 = 56 + 16 * √2 = 8 * (7 + 2 * √2) cm.

Answer: The perimeter of the trapezoid is 8 * (7 + 2 * √2) cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.