MHB Find AB:BC:CD | Quick & Easy Searching Tool

[Albert1]

find AB:BC:CD

 

[Albert1]

find AB:BC:CD

hint :

Spoiler

use law of sine,and find the ratio of area

 

[Albert1]

hint :

Spoiler

use law of sine,and find the ratio of area

more hint :

Spoiler

(1) find area of triangle ABP:CDP
(2) find area of triangle ACP:BDP

 

[Albert1]

find AB:BC:CD

solution of others

Spoiler

$\dfrac {\triangle ABP}{\triangle CDP}=\dfrac {12\times 9}{10\times 16}=\dfrac {27}{40}=\dfrac {AB}{CD}$
let $AB=27t, CD=40t,BC=k$
$\dfrac {\triangle APC}{\triangle BPD}=\dfrac {12\times 10}{9\times 16}=\dfrac {27t+k}{40t+k}=\dfrac {5}{6}$
we have $k=38t$
and $AB:BC:CD=27:38:40$