Question

What is the exact length of EC?

Answer 1

The calculated length of side EC is 2√130 km

How to determine the length of side EC

From the question, we have the following parameters that can be used in our computation:

The triangles

The triangles are similar triangles

So, we have

18/BC = 45/(21 + BC)

When evaluated, we have

BC = 14

the length of side EC is then calculated as

EC² = BC² + EB²

Substitute the known values into the equation

EC² = 14² + 18²

EC² = 520

Evaluate

EC = 2√130

Hence, the length of side EC is 2√130 km

Answer 2

2
`√(130)`

Explanation:

Δ ADC and Δ BEC are similar, thus the ratios of corresponding sides are equal, that is

`(AD)/(BE)` =
`(AC)/(BC)`, that is

`(45)/(18)` =
`(21+BC)/(BC)` ( 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 =
`√(520)` =
`√(4(130))` = 2
`√(130)`