Question

What is the exact length of EC?

A. 4√29/7 Feet
B.√164 Feet
C. 4√5 Feet
D. 2√41 Feet

Answer 1

• C.
  `4√(5)` feet

Explanation:

We have similar triangles:

• ΔADC ~ ΔBEC

Find segment BC using similarity and ratios:

• AD/ BE = AC / BC
• 28 / 8 = (10 + BC)/ BC
• 28BC = 8(10 + BC)
• 28BC = 8BC + 80
• 20BC = 80
• BC = 4

Find EC using Pythagorean:

• 
  `EC = √(BE^2+BC^2)=√(8^2+4^2)=√(64+16)=√(80)=4√(5)`

Correct choice is C