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BabaBlast [244]
2 years ago
11

Given: AKLM is a trapezoid, AK=13 LM=14, KL=5, AM=20 Find: h

Mathematics
1 answer:
Mama L [17]2 years ago
7 0

Answer:

  h = 11.2

Step-by-step explanation:

Let point M' be a point on AM that is 5 units toward point A from M. Let point B lie on AM such that KB⊥AM. Let x = AB; then BM' = 15 -x. The Pythagorean theorem gives rise to two equations in x and h:

  • x² + h² = AK² = 13²
  • (15-x)² + h² = M'K² = 14²

Subtracting the first from the second gives ...

  (225 -30x +x² + h²) - (x² + h²) = 196 -169

  225 -30x = 27

  x = 198/30 = 6.6

Then ...

  h = √(13² -x²) = √(169 -43.56) = √125.44

  h = 11.2

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