9)
Using intercept theorem
15/23 = TU/69
Multiplying both sides by 69, we get
15 ×69/23=TU
TU = 45
Similarly
23/36 =69/VW
Cross multiplying
23 VW = 36 × 69
Dividing by 23 on both sides
VW = 108
Now TW = 45 + 69 + 108
TW = 222
10)
VY= 34, YW = 6
So VW = 34 + 6 = 40
Using similarity we get
VY/VW = YZ/WX
34/40= 51/(2x²+10)
Cross multiplying
34(2x²+10) = 51 ×40
Dividing by 34 on both sides
2x² + 10 = 60
Subtracting 10
2x² = 50
x² = 25
x = 5
So WX = 2x² + 10 = 2(5)²+10 = 60
11)
By similarity
OE/OF = OG/OH
18/12 = 12/OH
Cross multiplying
18OH = 12 ×12
18OH =144
OH = 8
But H is on the negative X axis
So H(-8,0)
12)
From figure using similarity
x/187 = 620/220
Multiplying both sides by 187
We get
x = 527 ft
13)
Using angle bisector theorem
KJ/KL = JM/ML
x/63 = 28/x
Cross multiplying
x² = 63 ×28
x² = 1764
Taking square root
x = 42
So
Perimeter = 42 + 28 + 42 + 63
Perimeter = 175 units
