In an isosceles trapezoid, the bases are 8 dm and 14 dm, the height is 4 dm. Find the side of the trapezoid.
| July 3, 2021 | education
In an isosceles trapezoid, the bases are 8 dm and 14 dm, the height is 4 dm. Find the side of the trapezoid.
Given: ABCD – isosceles trapezoid, AB = CD, AD = 14 dm, AB = 8 dm, BK – height, BK = 4 dm.
Find: AB -?
Decision:
Consider a triangle AKB: ∠AKB = 90 (according to the problem statement). AK = (AD – BC) / 2 = (14 – 8) / 2 = 3 (dm). By the Pythagorean theorem: AB ^ 2 = BK ^ 2 + AK ^ 2
AB ^ 2 = 9 + 16 = 25
AB = √25 = 5
Answer 5 dm
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