8.3. Inscribed Similar Triangles http://www.ck12.org
Answers:
- Let’s set up a proportion.
shorter leg in 4 SV T
shorter leg in 4 RST=
hypotenuse in 4 SV T
hypotenuse in 4 RST
4
x=
x
20
x^2 = 80
x=√
80 = 4
√
5
- Use the Pythagorean Theorem.
y^2 +(
4
√
5
) 2
= 202
y^2 + 80 = 400
y^2 = 320
y=√
320 = 8
√
5
3.x=
√
18 · 54 =
√
18 · 18 · 3 = 18
√
3
- Use the Geometric Mean Theorems to solve forxandy.
20
x=
x
3515
y=
y
35
x^2 = 20 · 35 y^2 = 15 · 35
x=√
20 · 35 y=√
15 · 35
x= 10√
7 y= 5√
21
You could also use the Pythagorean Theorem to solve fory, oncexhas been solved for.
(
10
√
7
) 2
+y^2 = 352
700 +y^2 = 1225
y=√
525 = 5
√
21
Either method is acceptable.
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Use the diagram to answer questions 1-4.