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

Question

1103 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-21T11:49:25

As detailed below.

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.