Problem 1 :
Given : RV = 24
SU = 8
RS = ST = TU
RS = ?
Solution :
Let RS = x
From the condition.
SU = ST + TU
8 = x + x
8 = 2x
8/2 = x
4 = x
So, the value of RS is 4.
Problem 2 :
Given : RV = 24
SU = 8
RS = ST = TU
UV = ?
Solution :
From the condition.
SU = ST + TU
8 = x + x
8 = 2x
8/2 = x
4 = x
To find UV :
From the condition.
RV = RS + ST + TU + UV
24 = x + x + x + UV
24 = 3x + UV
24 = 3(4) + UV
24 = 12 + UV
24 - 12 = UV
UV = 12
Problem 3 :
Given : RV = 37
RS = TU
UV = 9
ST + UV = 15
ST = ?
RS = ?
SU = ?
Solution :
ST + UV = 15
ST + 9 = 15
ST = 15 - 9
ST = 6
RV = 37
Given condition : RS = TU
Let RS = x
RV = RS + ST + TU + UV
37 = x + 6 + x + 9
37 = 2x + 15
37 - 15 = 2x
22 = 2x
x = 22/2
x = 11
RS = 11
SU = ST + TU
SU = 6 + 11
SU = 17
So, the value of ST = 6, RS = 11, SU = 17.
Problem 4 :
Given : RV = 25
RT = 6
RS = ST = TU
UV = 3x + 1
x = ?
Solution :
From the condition.
RV = RT + UV
25 = 6 + 3x + 1
25 = 7 + 3x
25 - 7 = 3x
18 = 3x
18/3 = x
6 = x
So, the value of x is 6.
Problem 5 :
Points F, X, and D are collinear, with F between X and D. Draw a diagram and solve for X, if FX = 2x + 13, FD = 7x - 6, and XD = 2x + 70.
Solution :
Given, FX = 2x + 13, FD = 7x - 6, and XD = 2x + 70
XD = XF + FD
2x + 70 = 2x + 13 + 7x - 6
2x + 70 = 9x + 7
70 - 7 = 9x - 2x
63 = 7x
63/7 = x
x = 9
So, the value of x is 9.
Problem 6 :
P, A, and Z are collinear. Z is between P and A. Draw a diagram and solve for x, given : ZP = 6x - 13, ZA = 9x + 27, and AP = 3x + 74.
Solution :
Given ZP = 6x - 13, ZA = 9x + 27, and AP = 3x + 74
AP = ZP + ZA
3x + 74 = 6x - 13 + 9x + 27
3x + 74 = 15x + 14
74 - 14 = 15x - 3x
60 = 12x
x = 60/12
x = 5
So, the value of x is 5.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM