In an isosceles trapezoid, the height divides the larger base into segments of 5 and 12 cm
| May 14, 2021 | education
In an isosceles trapezoid, the height divides the larger base into segments of 5 and 12 cm, it is necessary to find the middle line.
The length of the segment АD = АН + DH = 5 + 12 = 17 cm.
Let’s draw the second height СK.
Since the trapezoid is isosceles, the ABН triangle is equal to the CDK triangle in the hypotenuse and acute angle, then DK = AH = 5 cm, and НK = BC = AD – AH – DK = 17 – 5 – 5 = 7 cm.
Let’s define the middle line of the trapezoid.
(ВС + АD) / 2 = (7 + 17) / 2 = 24/2 = 12 cm.
Answer: The middle line of the trapezoid is 12 cm.
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