Answer:
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
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! :)