Answer #10
s = 43
m = 9
LM and NO = 26
LO and MN = 43
Answer # 11
g = 11
f = 5
This is a square so all four sides are the same, each side length is 17
Step by step
#10
Parallelogram opposite sides are equal so we can make the expressions equal to solve
2m + 8 = 3m - 1
Subtract 2m from both sides
2m - 2m + 8 = 3m - 2m -1
8 = m - 1
Add 1 to each side
8 + 1 = m -1 + 1
9 = m
Sub value of m= 9 for each of these sides
2m + 8
2(9) + 8 = 26
3m - 1
3(9) -1 = 26
s + 1 = 5m - 2
Sub value of m=9
s + 1 = 5(9) -2
s + 1 = 43
subtract 1 from both sides
s + 1 -1 = 43 -1
s = 42
Left side = s + 1
42 + 1 = 43
Both sides (congruent) = 43
#11
This is a square so all four sides are the same, we can equal the left and right sides to find g
g + 6 = 2g -5
Subtract g from both sides
g - g + 6 = 2g - g -5
6 = g -5
Add 5 to both sides
6 + 5 = g -5 +5
g = 11
Now to find value of f
3f + 2 = 5f - 8
Subtract 3f from both sides
3f - 3f + 2 = 5f - 3f -8
2 = 2f -8
Add 8 to both sides
2 + 8 = 2f -8 +8
10 = 2f
Divide both sides by 2 to solve
10/2 = 2/2f
f = 5
Since this is a square, we only need to solve one side
g + 6 = side
11 + 6 = 17
Each side measures 17