1. similar
~ ~ ~

2. FJG GJH FGH
∆NLM ~ ∆LPM ~ ∆NPL

3. ADB BDC ABC BC AB 20 30
10√13
16.641
60√13 13
Exact
x =
16.641
Exact
60√13 13
(10√13)
16.641

4. G D E 8 10 6 F x
∆DGE ~ ∆FDE ~ ∆FGD FD DG DE GE = x 6 8 10 4 5
x = 4.8

5. length of hyp. of ∆FDE
length of shorter leg of ∆FEG 15 4 60 60
√4 × √15 = √60

6. C D CD CD
geometric mean
CD = √AD × BD DB
adjacent AD

7. 6.9 x
You could set the problem up this way too
6.9 = √5x
6.92 = 5x
9.522 ≈ x
6.9 x 5
9.522

8. y 24 9 =
y2 = 216
y = √216
y = √36 × √6
y = 6√6
4.5ft x
9.522ft
x = √9.522 × 4.5
x ≈ 6.546ft x
4.5
9.522 =
x2 =
x = √42.849
x ≈ 6.546ft or