Answer:
2[tex]\sqrt{130}[/tex]
Step-by-step explanation:
Δ ADC and Δ BEC are similar, thus the ratios of corresponding sides are equal, that is
[tex]\frac{AD}{BE}[/tex] = [tex]\frac{AC}{BC}[/tex], that is
[tex]\frac{45}{18}[/tex] = [tex]\frac{21+BC}{BC}[/tex] ( cross- multiply )
45BC = 18(21 + BC)
45BC = 378 + 18BC ( subtract 18BC from both sides
27BC = 378 ( divide both sides by 27 )
BC = 14
Using Pythagoras' identity in Δ BEC
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
EC² = 18² + 14² = 324 + 196 = 520 ( take the square root of both sides )
EC = [tex]\sqrt{520}[/tex] = [tex]\sqrt{4(130)}[/tex] = 2[tex]\sqrt{130}[/tex]
