70 points !
solve all of them

Question 2) L=52, W=13

Question 4) L=53, W=10

Question 6) 67 <-- Both are 67 :)

Question 8) Base angle= 23 1/3, Vertex angle = 66 2/3

Question 10) Base length = 11, other sides = 33

Question 12) Side 1= 15, Side 2= 13, Side 3= 21

Question 14) Side 1= 35, Side 2= 17.5, Side 3=22.5

Question 16) Angle X=99, Angle Y=52, Angle Z=29

Question 18) Length= 18, Width= 9

Step-by-step explanation:

Question 2:

1) We know:

W=1/4L

and

2L+2W=130

2) Plug in 1/4L as W in the second equation:

2L+2(1/4L)=130

3) Simplify:

2.5L=130

4) Divide both sides by 2.5:

L=52

5) Substitute 52 as L in the first equation:

W=13

Question 4:

1) We know:

L=5w+3

and

2L+2W=126

2) Substitute 5w+3 as L in the second equation:

2(5w+3)+2w=126

3) Distribute 2 to 5w and 3:

10w+6+2w=126

4) Combine alike terms:

12w+6=126

5) Subtract 6 from both sides:

12w=120

6) Divide both sides by 12:

w=10

7) Substitute 10 as w in the first equation:

L=53

Question 6:

1) We know:

Vertex angle = 46

2) Divide vertex angle by two by splitting triangle into two smaller triangles:

New angle= 23

3) Add the angles in the triangle:

23+90+x=180

4) Simplify:

113+x=180

5) Subtract 113 from both sides:

x=67

Question 8:

1) We know:

Vertex angle = 2B+20

Base angle = B

2) Add the angles in the triangle:

3B+20+90=180

3) Simplify:

3B+110=180

4) Subtract 110 from both sides:

3B=70

5) Divide both sides by 3:

B= 23 1/3

6) Substitute 23 1/3 as B in the original equation:

Vertex angle = 66 2/3

Question 10

1) We know:

non base sides = 3B

Perimeter=77

2) Add all the sides of the triangle to equal 77:

3B+3B+B=77

3) Simplify:

7B=77

4) Divide both sides by 7:

B=11

5) Substitute 11 as B in the original equation:

non base sides = 33

Question 12:

1) We know:

Perimeter=49

Side 2= A

Side 1= A+2

Side 3= 2A-5

2) Add all the sides to equal 49:

2A+A+A+2-5=49

3) Simplify:

4A-3=49

4) Add 3 to both sides:

4A=52

5) Divide both sides by 4:

A=13 <-- Side 2

6) Substitute 13 as A in sides 1 and 3:

Side 1= 15

Side 3= 21

Question 14

1) We know:

Perimeter=75

Side 1= 2A

Side 2= A

Side 3= A+5

2) Add all sides to equal 75:

2A+A+A+5=75

3) Simplify:

4A+5=75

4) Subtract 5 from both sides:

4A=70

5) Divide both sides by 4:

A=17.5

6) Substitute 17.5 as A in sides 1 and 3:

Side 1= 35

Side 3= 22.5

Question 16

1) We know:

Angle Z= 1/2Y+3

Angle Y= Y

Angle X= 4Z-17

2) Write all angles to equal 180:

4Z-17+Y+1/2Y+3=180

3) Substitute 1/2Y+3 as Z in the above equation:

4(1/2Y+3)-17+Y+1/2Y+3=180

4) Distribute 4 to 1/2Y and 3:

2Y+12-17+Y+1/2Y+3=180

5) Simplify:

3.5Y-2=180

6) Add 2 to both sides:

3.5Y=182

7) Divide both sides by 3.5:

Y=52

8) Substitute 52 as Y in Angle Z's equation:

Z=29

9) Substitute 29 as Z in Angle X's equation:

X=99

Question 18:

1) We know:

Perimeter=54

Width= L+2

Length= 3L-3

2) Add 2L+2W to equal 54:

2(L+2)+2(3L-3)=54

3) Distribute 2 to L and 2:

2L+4+2(3L-3)=54

4) Distribute 2 to 3L and -3:

2L+4+6L-6=54

5) Simplify:

8L-2=54

6) Add 2 to both sides:

8L=56

7) Divide both sides by 8:

L=7

8) Substitute 7 as L in the original equations:

Width= 9

Length= 18

Let me know if you have any questions! :)

step-by-step explanation: