A straight line drawn parallel to the side of the trapezoid through the end of the smaller

univerkov | July 23, 2021 | education

A straight line drawn parallel to the side of the trapezoid through the end of the smaller base, equal to 34, cuts off the triangle, the perimeter of which is 69. Find the perimeter of the trapezoid.

Since the CH segment is parallel to AB, ABCH is a parallelogram, then AH = BC = 34 cm, AB = CH.

The perimeter of the trapezoid is: Ravsd = AB + BC + CD + AD = CH + BC + CD + AH + DH = (CH + CD + DH) + BC + AH.

The perimeter of the triangle CHD is equal to: Psnd = CH + CD + DH.

Then Ravsd = Rsdn + 2 * BC = 69 + 2 * 34 = 137 cm.

Answer: The perimeter of the trapezoid is 137 cm.

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