The bases of the rectangular trapezoid are 2 cm and 10 cm, and the sides are in a ratio of 3: 5.

| June 20, 2021 | education

The bases of the rectangular trapezoid are 2 cm and 10 cm, and the sides are in a ratio of 3: 5. Find the perimeter of the trapezoid.

From the vertex C of the trapezoid, we will construct the height CH.

Since the trapezoid is rectangular, and CH is its height, then the quadrangle ABCH is a rectangle, and then AH = BC = 2 cm, CH = AB.

The length of the segment DH = AD – AH = 10 – 2 = 8 cm.

Let the side length AB = 3 * X cm, then, by condition, CD = 5 * X cm.

CH = 3 * X cm.

In a right-angled triangle CDH DH ^ 2 = CD ^ 2 – CH ^ 2.

64 = 25 * X ^ 2 – 9 * X ^ 2 = 16 * X ^ 2.

X2 = 64/16 = 4.

X = 2, then AB = CH = 2 * 3 = 6 cm.

CD = 5 * 2 = 10 cm.

Determine the perimeter of the trapezoid.

P = 6 + 2 + 10 + 10 = 28 cm.

Answer: The perimeter of the trapezoid is 28 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.