Triangle jlk be a right triangle with right angle l. if jm=3 and and mk equals 6 find lm show work

The length of LM is 4.24

Step-by-step 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