Answer with Step-by-step explanation:
1.In triangle ABC
AB=BC
Let AB=BC=x and AC=y
Perimeter of triangle ABC=25
![x+x+y=25](/tpl/images/0446/6702/1d227.png)
...(1)
...(2)
Adding equation (1) and (2)
![3x=29](/tpl/images/0446/6702/2958b.png)
![x=\frac{29}{3}=9.67](/tpl/images/0446/6702/8159e.png)
Substitute x=9.67 in equation (2)
![9.67-y=4](/tpl/images/0446/6702/a29a9.png)
![y=9.67-4=5.67](/tpl/images/0446/6702/07a73.png)
![AB=BC=9.67](/tpl/images/0446/6702/22402.png)
![AC=5.67](/tpl/images/0446/6702/db88a.png)
2.![m\angle R=2x+11](/tpl/images/0446/6702/e94b4.png)
![m\angle S=3x+23](/tpl/images/0446/6702/ac08d.png)
![m\angle T=x+42](/tpl/images/0446/6702/36fb3.png)
![m\angle R+m\angle S+m\angle T=180^{\circ}](/tpl/images/0446/6702/60c3b.png)
By using triangle angle sum property
Substitute the values then we get
![3x+42+4x-11+x+13=180](/tpl/images/0446/6702/f0a95.png)
![8x+44=180](/tpl/images/0446/6702/12acc.png)
![8x=180-44=136](/tpl/images/0446/6702/a2083.png)
![x=\frac{136}{8}=17](/tpl/images/0446/6702/c3ba4.png)
Substitute the value
![m\angle R=3(17)+42=93^{\circ}](/tpl/images/0446/6702/74ac9.png)
![m\angle S=4(17)-11=57^{\circ}](/tpl/images/0446/6702/20487.png)
![m\angle T=17+13=30^{\circ}](/tpl/images/0446/6702/85826.png)
![m\angle Rm\angle S](/tpl/images/0446/6702/efed5.png)
![m\angle Sm\angle T](/tpl/images/0446/6702/a52eb.png)
(Side ST is opposite to angle R, Side RT is opposite to angle S
(side RS is opposite to angle T)
When a>b
Then , opposite side of a> opposite side of b
RS<RT<ST
3.![m\angle R=2x+11](/tpl/images/0446/6702/e94b4.png)
![m\angle S=3x+23](/tpl/images/0446/6702/ac08d.png)
![\angle T=x+42](/tpl/images/0446/6702/39cb3.png)
![m\angle R+m\angle S+m\angle T=180^{\circ}](/tpl/images/0446/6702/60c3b.png)
By using triangle angle sum property
Substitute the values then we get
![2x+11+3x+23+x+42=180](/tpl/images/0446/6702/7cb7f.png)
![6x+76=180](/tpl/images/0446/6702/c35e8.png)
![6x=180-76](/tpl/images/0446/6702/2af43.png)
![6x=104](/tpl/images/0446/6702/cf810.png)
![x=\frac{104}{6}=17.3](/tpl/images/0446/6702/9330c.png)
Substitute the value
![m\angle R=2(17.3)+11=45.6](/tpl/images/0446/6702/9c551.png)
![m\angle S=3(17.3)+23=74.9](/tpl/images/0446/6702/1f844.png)
![m\angle T=17.3=42=59.3](/tpl/images/0446/6702/8da29.png)
![m\angle Sm\angle T](/tpl/images/0446/6702/a52eb.png)
![m\angle Tm\angle R](/tpl/images/0446/6702/53967.png)
RT>RS
RS>ST
ST<RS<RT