In an isosceles trapezoid, the bases are 8 cm and 48 cm, diagonal is 35 cm Find the perimeter of the trapezoid.

univerkov | July 5, 2021 | education

Let’s build the height of the CH trapezoid.

According to the property of the height of an isosceles trapezoid, the length of the segment is DH = (AD – BC) / 2 = (48 – 8) / 2 = 20 cm.

Then the length of the segment АН = АD – DH = 48 – 20 = 28 cm.

In a right-angled triangle ACH, then CH ^ 2 = AC ^ 2 – AD ^ 2 = 35 ^ 2 – 28 ^ 2 = 1225 – 784 = 441.

CH = 21 cm.

From the right-angled triangle СDН we determine the length of the hypotenuse СD.

CD ^ 2 = CH ^ 2 + DH ^ 2 = 441 + 400 = 841.

СD = 29 cm.

Since the trapezoid is isosceles, then AB = CD = 29 cm.

Determine the perimeter of the trapezoid.

Ravsd = (AB + BC + CD + AD) = (29 + 8 + 29 + 48) = 114 cm.

Answer: The perimeter of the trapezoid is 114 cm.

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