Question

Can someone help me find the ratio for the sides of this triangle?

Answer 1

As detailed below.

Explanation:

Given `DE` parallel `AB`

Consider triangles CDE & CAB.

`hat(CDE) = hat(CAB)` ( corresponding angles.

`hat(CED) = hat(CBA)` ( corresponding angles.

`hat C` common.

Hence, two triangles are similar.

`:. (AC) / (DC) = (BC) / (EC) = (AB) / (DE)` Eqn (1)

(6.) but `AC = AD + DC` and `BC = (BE + EC)`

`:. (AD+ DC) / ((DC) = (BE + EC) / (EC)`

`(AD) / (DC) + cancel1 = (BE) / (EC) + cancel1`

`(AD) / (DC) = (BE) / (EC)`

But given `(AD) / (DC) = 1/3`

`:. (EB) / (EC) = 1/3` or `(EC) / (EB) = 3 / 1 = 3`

(7.) Measurements are known for `AB, AD, BC`

Substituting in (1),

`(color(purple )(AD) + DC) / (DC) = color(purple)(BC) / (EC) = color(purple)(AB) / (DE)`

Hence, at least one more side measurement is needed to find the lengths of other sides.