The slopes of the isosceles trapezoid are 8 cm and 16 cm, and the side is related to the height as 5: 3.

| September 11, 2021 | education

The slopes of the isosceles trapezoid are 8 cm and 16 cm, and the side is related to the height as 5: 3. Find the perimeter of the trapezoid.

From the top of the isosceles trapezoid, we will construct the height CH.

The height CH divides the larger base AD into two segments, the length of the smaller of which is equal to the half-difference of the lengths of its bases.

DН = (АD – ВС) / 2 = (16 – 8) / 2 = 8/2 = 4 cm.

Let the length of the side side be 5 * X cm, then the height CH = 3 * X cm.

In a right-angled triangle СDН, according to the Pythagorean theorem, СD ^ 2 = CH ^ 2 + DH ^ 2.

25 * X ^ 2 = 9 * X ^ 2 + 16.

16 + X ^ 2 = 16.

X = 1.

Then CD = AB = 1 * 5 = 5 cm.

Then Ravsd = AB + BC + CD + AD = 5 + 8 + 5 + 16 = 34 cm.

Answer: The perimeter of the trapezoid is 34 cm.



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