1)
you have similar triangles(ABC, ADE), so their side length ratios are equal

8/2=4/CE
CE*4=4
CE=1

2)
angle bisector theorem:
CD/DA=BC/BA

CD/DA=10/8
I:AD=10CD/8

we also know AC=AD+CD=6
II:CD=6-AD

insert II in I:

AD=10(6-AD)/8
=5(6-AD)/4
=(30-5AD)/4
4AD=30-5AD
9AD=30
3AD=10
AD=10/3

8 0

2 years ago

Rashau made a rectangular frame for her latest oil painting. The length is 28 centimeters more than triple the width. The perime

postnew [5]

The length is about 28 more than three times the width. Denoted as (a) width, and as (b) the length. Then move on to lay the system of equations, as done below:

$\begin{cases}2a+2b=136\\b=3a+28\end{cases}$
$\begin{cases}2a+2b=136|:2\\b=3a+28\end{cases}$
$\begin{cases}a+b=68\\b=3a+28\end{cases}$
$\begin{cases}a+3a+28=68\\b=3a+28\end{cases}$
$\begin{cases}4a=40|:4\\b=3a+28\end{cases}$
$\begin{cases}a=10\\b=3*10+28\end{cases}$
$\begin{cases}a=10\\b=58\end{cases}$

The short side has a length of 10 cm, and 58 cm long.

5 0

3 years ago