Question

Find the value of x so that BC II DE

Answer 1

x = 10

Explanation:

if BC and DE are parallel then the sides of the triangle are divided proportionally, that is

`(CE)/(AE)` =
`(BD)/(AD)` ( substitute values )

`(x-2)/(16)` =
`(x-3)/(14)` ( cross- multiply )

16(x - 3) = 14(x - 2) ← distribute parenthesis

16x - 48 = 14x - 28 ( subtract 14x from both sides )

2x - 48 = - 28 ( add 48 to both sides )

2x = 20 ( divide both sides by 2 )

x = 10

then for BC and DE to be parallel, x has the value x = 10