Question

Please help asap! BAC~DEC x=___ units?

Answer 1

x = 3 units

Explanation:

These two triangles are similar figures, which means the ratio of the lengths of their corresponding sides are equal:

`(Side AB)/(Side AC) = (Side DE)/(Side CE)`

=
`(24)/(2x) = (56)/(3x + 5)`

Cross-multiplication is applied:

=
`(24)(3x + 5) = (56)(2x)`

Parenthesis are expanded by using the Distributive Law:

=
`72x + 120 = 112x`

Bring all the like terms together and then isolate x:

=
`120 = 112x - 72x`

=
`120 = 40x`

= x =
`(120)/(40)`

∴ x = 3 units