Question

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

Answer 1

h = 11.2

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