The bases of the rectangular trapezoid are 14cm and the large diagonal is the bisector

The bases of the rectangular trapezoid are 14cm and the large diagonal is the bisector of the right angle. Find the perimeter of the trapezoid.

Since BD, by condition, is the bisector of a right angle, then the angle ABD = 90/2 = 45, the angle ADB = (180 – 90 – 45) = 45, then the triangle ABD is rectangular and isosceles, AB = AD = 24 cm.

Let’s build the height of the CH.

Quadrangle ABCN is a rectangle, then CH = AB = 24 cm, AH = BC = 14 cm.

DН = АD – АН = 24 – 14 = 10 cm.

Then, by the Pythagorean theorem, from the right-angled triangle СDН:

CD ^ 2 = CH ^ 2 + DH ^ 2 = 576 + 100 = 676.

СD = 26 cm.

Determine the perimeter of the trapezoid.

Ravsd = 24 + 14 + 26 + 24 = 88 cm.

Answer: The perimeter of the trapezoid is 88 cm.