Question

Triangle ABC has a right angle at angle c and pounts e,d and f are midpoints. Line df = 3 and line segment ab= 10. What is the length of line ed?

Answer 1

See the attached figure.
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AB = 10 , FD = 3
∵ D is the midpoint of AB, and F is the mid point of CB
∴ FD // AC , FD = 0.5 AC
∵ Δ ABC is a right triangle at C
∴ FD ⊥ BC
∴ BD = 0.5 AB = 5
∴ in Δ FDB ⇒⇒ BF² = BD² - FD² = 5² - 3² = 16
∴ BF = √16 = 4
∵ F is the mid point of CB 
∴ CF = BF = 4 , and CB = 2 BF = 2*4 = 8
∵ D is the midpoint of AB, and E is the mid point of AC
∴ DE // CB  , and DE = 0.5 CB = 0.5 * 8 = 4

∴ The length of line ED is 4