Answer:
The length of LM is 4.24
Explanation:
* Lets revise the rules in the right angle triangle when we draw the
perpendicular from the right angle to the hypotenuse
- In triangle ABC
# Angle B is a right angle
# The hypotenuse is AC
# BD ⊥ AC
∴ (AB)² = AD × AC
∴ (BC)² = CD × AC
∴ (BD)² = AD × CD
∴ BD × AC = AB × BC
* Lets use one of these rules to solve the problem
∵ Δ JLK is a right triangle
∵ ∠L is a right angle
∵ LM ⊥ JK
- We can find LM by one of the rule above
∵ JM = 3
∵ MK = 6
∵ (LM)² = JM × KM
∴ (LM)² = 3 × 6 = 18 ⇒ take a square root for both sides
∴ LM = √18 = 3√2 ≅ 4.24
* The length of LM is 4.24